CMB Anisotropy Research Articles

Dual inflation and bounce cosmologies interpretation of pulsar timing array data

We explore a dual scenario of generalized inflation and bounce cosmologies, producing a scale-invariant curvature perturbation spectrum. Bayesian analysis with pulsar timing array data identifies, for the first time, viable regions from inflation and bounce that simultaneously explain stochastic gravitational wave background (SGWB) signals and CMB anisotropies. Bayes factor calculations strongly favor this dual scenario over conventional sources and provide initial evidence of a duality between inflation and bounce regarding SGWB, offering new insights for early universe model-building and future observations.

LiteBIRD science goals and forecasts: primordial magnetic fields

We present detailed forecasts for the constraints on the characteristics of primordial magnetic fields (PMFs) generated prior to recombination that will be obtained with the LiteBIRD satellite. The constraints are driven by some of the main physical effects of PMFs on the CMB anisotropies: the gravitational effects of magnetically-induced perturbations; the effects on the thermal and ionization history of the Universe; the Faraday rotation imprint on the CMB polarization spectra; and the non-Gaussianities induced in polarization anisotropies. LiteBIRD represents a sensitive probe for PMFs.We explore different levels of complexity, for LiteBIRD data and PMF configurations, accounting for possible degeneracies with primordial gravitational waves from inflation. By exploiting all the physical effects, LiteBIRD will be able to improve the current limit on PMFs at intermediate and large scales coming from Planck. In particular, thanks to its accurate B-mode polarization measurement, LiteBIRD will improve the constraints on infrared configurations for the gravitational effect, giving B n B=-2.9 1 Mpc< 0.8 nG at 95% C.L., potentially opening the possibility to detect nanogauss fields with high significance. We also observe a significant improvement in the limits when marginalized over the spectral index, B n Bmarg 1 Mpc< 2.2 nG at 95 % C.L. From the thermal history effect, which relies mainly on E-mode polarization data, we obtain a significant improvement for all PMF configurations, with the marginalized case, √⟨B 2⟩marg<0.50 nG at 95 % C.L. Faraday rotation constraints will take advantage of the wide frequency coverage of LiteBIRD and the high sensitivity in B modes, improving the limits by orders of magnitude with respect to current results, B n B=-2.9 1 Mpc < 3.2 nG at 95 % C.L. Finally, non-Gaussianities of the B-mode polarization can probe PMFs at the level of 1 nG, again significantly improving the current bounds from Planck. Altogether our forecasts represent a broad collection of complementary probes based on widely tested methodologies, providing conservative limits on PMF characteristics that will be achieved with the LiteBIRD satellite.

Constraining ultra slow roll inflation using cosmological datasets

In recent years, the detection of gravitational waves by LIGO and PTA collaborationshave raised the intriguing possibility of excess matter power at small scales. Such anincrease can be achieved by ultra slow roll (USR) phase during inflationary epoch.We constrain excess power over small scales within the framework of such models usingcosmological datasets, particularly of CMB anisotropies and Lyman-α.We parameterize the USR phase in terms of thee-fold at the onset of USR (counted from the end of inflation) N̅1 andthe duration of USR phase Δ N.The former dictates the scale of enhancement in the primordial power spectrum, while the latter determines the amplitude of such anenhancement.From a joint dataset of CMB and galaxy surveys, we obtainN̅1 ≲ 45 with no bound on Δ N. This in turn implies thatthe scales over which the power spectrum can deviate significantly from thenearly scale invariant behavior of a typical slow-roll model isk ≳1 Mpc-1.On the other hand, the Lyman-α data is sensitive to baryonic powerspectrum along the line of sight. We consider a semi-analytic theoretical methodand high spectral-resolution Lyman-α data to constrain the model.The Lyman-α data limits both the USR parameters:N̅1 ≲ 41 and Δ N ≲ 0.4.This constrains the amplitude of the power spectrum enhancement to be less thana factor of hundred over scales 1 ≲ k/ Mpc-1≲ 100,thereby considerably improving the constraint on power over these scales ascompared to the bounds arrived at from CMB spectral distortion.

Particle dark matter versus modified gravity

There are at least two possible solutions to the so-called Dark Matter problem. One is to introduce new particles and another one is to modify gravity. In these proceedings of the 182nd Nobel Symposium on dark matter, I question the particle dark matter hypothesis in light of new developments in the gravity sector. To this effect, I review how the CMB anisotropies and the details of structure formation have been used to test the dark matter microscopic properties. I explain how this has led to challenge the Hut-Lee & Weinberg argument and the introduction of light (thermal) dark matter scenarios and dark photon/light Z′. These developments have ultimately paved the way for a comprehensive exploration of the entire dark matter mass spectrum. I then discuss a new theory of modified gravity that appears to be a novel alternative to particle dark matter and ask the question: how to distinguish the two? I expect this question to become extremely relevant in absence of dark matter particle detection in Earth based experiments and in presence of ambiguous astrophysical and cosmological signals.

CRRfast: an emulator for the cosmological recombination radiation with effects from inhomogeneous recombination

ABSTRACT The cosmological recombination radiation (CRR) is one of the guaranteed ΛCDM spectral distortion (SD) signals. Even if very small in amplitude, it provides a direct probe of the three recombination eras, opening the path for testing one of the key pillars in our cosmological interpretation of the measured CMB anisotropies. Here, we develop a new emulator, CRRfast, to quickly and accurately represent the CRR for a wide range of cosmologies, using the state-of-the-art CosmoSpec code as a reference. CRRfast has been made publicly available both as stand-alone code and as part of class, thereby completing the set of average ΛCDM sources of SDs that can be modelled with class. With this newly developed pipeline we investigate the full constraining power of SDs within ΛCDM and highlight possible future applications to experimental design optimization. Furthermore, we show that the inhomogeneous evolution of the recombination process imprints second-order contributions to the CRR spectrum, leading to a broadening and shifting of the CRR features. These second-order terms are naturally captured by the emulator and allow us to evaluate the contribution of the ΛCDM primordial perturbations to the average CRR as well as to illustrate the effect of perturbed recombination due to Primordial Magnetic Fields (PMFs). As it turns out, while the second-order ΛCDM signal can be neglected, it could be significantly enhanced in the beyond-ΛCDM models. In particular in the case of PMFs, we demonstrate that through these non-linear terms the parameter space relevant to the Hubble tension could be tested with future CMB spectrometers.

Estimating Baryon Density through the CAMB and Assessing its Reliability

The Cosmic Microwave Background Radiation and its anisotropies allow us to analyze many properties and phenomena of the early universe. One such important property is the Baryon Density(Ω_b), a cosmological constant for the density of Baryons in the universe in comparison to its critical density. Baryon Density affects the interactions of matter in the early universe and therefore the analysis of CMB Anisotropies to study how matter interacts allows for the estimation of the Baryon Density in the Early Universe. Understanding Ω_b, is crucial as it reveals information about the composition of the universe, such as the amount of dark matter and dark energy, the early formation of celestial bodies and matter-antimatter asymmetry. This paper aimed to test the reliability of CAMB, a simulation algorithm for CMB anisotropies, by estimating Ω_b h^2. The CAMB mainly utilizes a combination of field equations, the Friedmann-Lemaître-Robertson-Walker metric, Fluid Equations, the Boltzmann Equation and Linear Perturbation theory in order to compute the CMB power spectra. We estimated the value of Ω_b h^2, maintaining other cosmological parameters constant and changing Ω_b h^2 from 0.01 to 0.03 in increments of 0.000625. The peaks, troughs, positions, damping scale and amplitudes of the resultant TT and TE power spectra were compared with data from the Planck Satellite. We use chi-square minimization and find the best fit value and uncertainty forΩ_b h^2 to be 0.02325 ± 0.00015. The estimated value of the baryon density from our study was compared to existing estimates to evaluate the reliability of CAMB as a simulation and source of information for further CMB Anisotropy related research, where it was confirmed to be accurate. However, further developments using wider sets of data was acknowledged with deep learning being a potential step forward.

Theoretically Motivated Dark Electromagnetism as the Origin of Relativistic Modified Newtonian Dynamics

The present paper is a modest attempt to initiate the research program outlined in this abstract. We propose that general relativity and relativistic MOND (RelMOND) are analogues of broken electroweak symmetry. That is, SU(2)R×U(1)YDEM→U(1)DEM (DEM stands for dark electromagnetism), and GR is assumed to arise from the broken SU(2)R symmetry and is analogous to the weak force. RelMOND is identified with dark electromagnetism U(1)DEM, which is the remaining unbroken symmetry after the spontaneous symmetry breaking of the dark electro-grav sector SU(2)R×U(1)YDEM. This sector, as well as the electroweak sector, arises from the breaking of an E8×E8 symmetry in a recently proposed model of unification of the standard model with pre-gravitation, with the latter based on an SU(2)R gauge theory. The source charge for the dark electromagnetic force is the square root of mass, motivated by the experimental fact that the ratio of the square roots of the masses of the electron, up-quark, and down-quark is 1:2:3, which is the opposite of the ratio of their electric charges at 3:2:1. The introduction of the dark electromagnetic force helps us understand the peculiar mass ratios of the second and third generations of charged fermions. We also note that in the deep MOND regime, acceleration is proportional to the square root of mass, which motivates us to propose the relativistic U(1)DEM gauge symmetry as the origin of MOND. We explain why the dark electromagnetic force falls inversely with distance, as in MOND, rather than following the inverse square of distance. We conclude that dark electromagnetism effectively mimics cold dark matter, and the two are essentially indistinguishable in cosmological situations where CDM successfully explains observations, such as CMB anisotropies and gravitational lensing.

Study of Nonlinear Evolution of Spacetime Fluctuations in Quantum Gravity Inflation for Deriving Primordial Spectrum

We study the evolution of quantum fluctuations of gravity around an inflationary solution in renormalizable quantum gravity, in which the initial scalar-fluctuation dominance is shown by the background-free nature expressed by a special conformal invariance. Inflation ignites at the Planck scale and continues until spacetime phase transition occurs at a dynamical scale of about 1017 GeV. We show that during inflation, the initially large scale-invariant fluctuations reduce in amplitude to the appropriate magnitude suggested by tiny CMB anisotropies. The goal of this research is to derive the spectra of scalar fluctuations at the phase transition point, that is, the primordial spectra. A system of nonlinear evolution equations for the fluctuations is derived from the quantum gravity effective action. The running coupling constant is then expressed by a time-dependent average following the spirit of the mean field approximation. In this paper, we determine and examine various nonlinear terms, not treated in previous studies such as the exponential factor of the conformal mode. These contributions occur during the early stage of inflation when the amplitude is still large. Moreover, in order to verify their effects concretely, we numerically solve the evolution equation by making a simplification to extract the most contributing parts of the terms in comoving momentum space. The result indicates that they serve to maintain the initial scale invariance over a wide range beyond the comoving Planck scale. This is a challenge toward the derivation of the precise primordial spectra, and we expect in the future that it will lead to the resolution of the tensions that have arisen in cosmology.

Disentangling the primordial nature of stochastic gravitational wave backgrounds with CMB spectral distortions

ABSTRACT The recent detection of a stochastic gravitational wave background (SGWB) at nanohertz frequencies by pulsar timing arrays (PTAs) has sparked a flurry of interest. Beyond the standard interpretation that the progenitor is a network of supermassive black hole binaries, many exotic models have also been proposed, some of which can potentially offer a better fit to the data. We explore how the various connections between gravitational waves (GWs) and cosmic microwave background (CMB) spectral distortions (SDs) can be leveraged to help determine whether an SGWB was generated primordially or astrophysically. To this end, we present updated k-space window functions that can be used for distortion parameter estimation on enhancements to the primordial scalar power spectrum. These same enhancements can also source GWs directly at second order in perturbation theory, so-called scalar-induced GWs (SIGWs), and indirectly through the formation of primordial black holes (PBHs). We perform a mapping of scalar power spectrum constraints into limits on the GW parameter space of SIGWs for δ-function features. We highlight that broader features in the scalar spectrum can explain the PTA results while simultaneously producing an SD within reach of future experiments. We additionally update PBH constraints from μ- and y-type SDs. Refined treatments of the distortion window functions widen existing SD constraints, and we find that a future CMB spectrometer could play a pivotal role in unravelling the origin of GWs imprinted at or below CMB anisotropy scales.

The pairwise and cross-pairwise y-type polarised kinetic Sunyaev Zeldovich effect from transverse velocity of galaxy clusters

We develop a new theoretical framework for studying the pairwise and cross-pairwise polarised kinetic Sunyaev Zeldovich (pkSZ) effect arising from the transverse peculiar velocity of galaxy clusters. The pkSZ effect is second order in peculiar velocities and has a spectrum that can be decomposed into y-type and blackbody components, whereas the unpolarised linear kSZ effect has only the blackbody component. Thus, the detectability of the pkSZ effect depends only on the sensitivity and the number of frequency channels of the survey and not on the other primary and secondary CMB anisotropies. We consider pairing of clusters with other clusters as well as cross-pairing of clusters with galaxies from spectroscopic galaxy surveys. The pairwise pkSZ signal is a function of intra-pair spatial separation. We develop and compare estimators of the pairwise pkSZ effect and study the detectability of the pairwise signal with cluster catalogs consisting of a few hundred thousand clusters expected from surveys such as eROSITA and CMB-S4. We find that cross-pairing clusters with galaxies from a large overlapping spectroscopic survey having a few billion galaxies will enable us to detect the pairwise pkSZ effect with CMB-S4. The pairwise pkSZ effect will thus open up a new window into the large-scale structure of the Universe in the coming decades.

Do the early galaxies observed by JWST disagree with Planck's CMB polarization measurements?

The recent observations from the James Webb Space Telescope have led to a surprising discovery of a significant density of massive galaxies with masses of M ≥ 1010.5 M ⊙ at redshifts of approximately z ∼ 10. This corresponds to a stellar mass density of roughly ρ * ∼ 106 M ⊙ Mpc-3. Despite making conservative assumptions regarding galaxy formation, this finding may not be compatible with the standard ΛCDM cosmology that is favored by observations of CMB Anisotropies from the Planck satellite. In this paper, we confirm the substantial discrepancy with Planck's results within the ΛCDM framework. Assuming a value of ϵ = 0.2 for the efficiency of converting baryons into stars, we indeed find that the ΛCDM model is excluded at more than 99.7 % confidence level (C.L.). An even more significant exclusion is found for ϵ ∼ 0.1, while a better agreement, but still in tension at more than 95 %, is obtained for ϵ = 0.32.This tension, as already discussed in the literature, could arise either from systematics in the JWST measurements or from new physics. Here, as a last-ditch effort, we point out that disregarding the large angular scale polarization obtained by Planck, which allows for significantly larger values of the matter clustering parameter σ 8, could lead to better agreement between Planck and JWST within the ΛCDM framework. Assuming ΛCDM and no systematics in the current JWST results, this implies either an unknown systematic error in current large angular scale CMB polarization measurements or an unidentified physical mechanism that could lower the expected amount of CMB polarization produced during the epoch of reionization. Interestingly, the model compatible with Planck temperature-only data and JWST observation also favors a higher Hubble constant H 0 = 69.0±1.1 km/s/Mpc at 68% C.L., in better agreement with observations based on SN-Ia luminosity distances.

QUIJOTE scientific results – X. Spatial variations of Anomalous Microwave Emission along the Galactic plane

ABSTRACT Anomalous microwave emission (AME) is an important emission component between 10 and 60 GHz that is not yet fully understood. It seems to be ubiquitous in our Galaxy and is observed at a broad range of angular scales. Here we use the new QUIJOTE-MFI wide survey data at 11, 13, 17, and 19 GHz to constrain the AME in the Galactic plane (|b| &amp;lt; 10°) on degree scales. We built the spectral energy distribution between 0.408 and 3000 GHz for each of the 5309 0.9° pixels in the Galactic plane, and fitted a parametric model by considering five emission components: synchrotron, free–free, AME, thermal dust and CMB anisotropies. We show that not including QUIJOTE-MFI data points leads to the underestimation (up to 50 per cent) of the AME signal in favour of free–free emission. The parameters describing these components are then intercompared, looking for relations that help to understand AME physical processes. We find median values for the AME width, WAME, and for its peak frequency, νAME, respectively of $0.560^{+0.059}_{-0.050}$ and $20.7^{+2.0}_{-1.9}$ GHz, slightly in tension with current theoretical models. We find spatial variations throughout the Galactic plane for νAME, but only with reduced statistical significance. We report correlations of AME parameters with certain ISM properties, such as that between the AME emissivity (which shows variations with the Galactic longitude) and the interstellar radiation field, and that between the AME peak frequency and dust temperature. Finally, we discuss the implications of our results on the possible molecules responsible for AME.

Constraints on the spectral signatures of superconducting cosmic strings

ABSTRACT If they exist, networks of superconducting cosmic strings are capable of injecting copious amounts of electromagnetic energy into the background over a broad range of frequencies. We study this injection both analytically, as well as numerically using the thermalization code CosmoTherm. With our refined analytic formalism, we update constraints from CMB spectral distortions by following the injection of entropy, as well as energy, on the amplitude of the μ-distortion, leading to a significant improvement in those limits. Furthermore, we utilize the full shape of the distorted spectrum from CosmoTherm to include constraints from non-μ, non-y type distortions. Additionally, we use the outputs for the ionization history and global 21-cm signal to derive and update constraints on string model parameters using measurements from other data sets. Analysis of CMB anisotropies provides the most stringent constraints, though with a slightly modified shape and strength when compared to previous results. Modifications of the reionization history provide new bounds in the high current domain, and we also find that the observations of the low-frequency radio background probe a small region of parameter space not explored by other data sets. We also analyse global 21-cm constraints, and find that the inclusion of soft photon heating plays a crucial role, essentially removing any constraints in the considered parameter domain. Spectral distortion measurements from COBE/FIRAS are covered by other constraints, but our conservative forecast shows that a PIXIE-type satellite would probe important unexplored regions of parameter space.

Formula omitted] gravity with broken Weyl gauge symmetry, cosmological backreaction, and its effects on CMB anisotropy

We propose a new class of f(R) theory where its Weyl gauge symmetry is broken in the primordial era of the universe. This symmetry forces one to adopt a new scalar field, namely a Weyl field and a gauge vector boson. Furthermore, an equivalent form of the Einstein–Hilbert Lagrangian with a non-minimally coupled scalar field corresponding to the function f(R) is found. Due to the geometrical feature of the Weyl field, it turns out that the symmetry breaking induces a non-minimal coupling, which cannot be expected in the standard f(R) theories. We explain how this affects the evolution of the universe at cosmological scales. It is shown that there may be a value shift in the Planck constant and the cosmological constant. This can be regarded as a genuine exemplification of the cosmological backreaction. Furthermore, one also finds new features in the evolution of perturbational variables and cosmic microwave background anisotropy. Moreover, we prove that when a specific f(R) model invokes inflation, the amplitude of the primordial gravitational waves affects the evolution of scalar perturbation due to the new non-minimal coupling. As a case study, we explain how this can be embodied in the Starobinsky inflation. Finally, we discuss some impacts that this physics can bear and the possibility of giving a new restriction of the estimation of cosmological variables such as the gravitational wave amplitude with experiments.

Hydrodynamical structure formation in Milgromian cosmology

ABSTRACT We present the first hydrodynamical cosmological simulations in the νHDM framework based on Milgromian dynamics (MOND) with light (11 eV) sterile neutrinos. νHDM can explain the expansion history, CMB anisotropies, and galaxy cluster dynamics similarly to standard cosmology while preserving MOND’s successes on galaxy scales, making this the most conservative Milgromian framework. We generate initial conditions including sterile neutrinos using camb and music and modify the publicly available code phantom of ramses to run νHDM models. The simulations start at redshift $z_e$ = 199, when the gravitational fields are stronger than $a_{_0}$ provided this does not vary. We analyse the growth of structure and investigate the impact of resolution and box size, which is at most 600 comoving Mpc. Large density contrasts arise at late times, which may explain the KBC void and Hubble tension. We quantify the mass function of formed structures at different redshifts. We show that the sterile neutrino mass fraction in these structures is similar to the cosmic fraction at high masses (consistent with MOND dynamical analyses) but approaches zero at lower masses, as expected for galaxies. We also identify structures with a low peculiar velocity comparable to the Local Group, but these are rare. The onset of group/cluster-scale structure formation at $z_e$ ≈ 4 appears to be in tension with observations of high redshift galaxies, which we discuss in comparison to prior analytical work in a MONDian framework. The formation of a cosmic web of filaments and voids demonstrates that this is not unique to standard Einstein/Newton-based cosmology.

Constraints on the phase transition of early dark energy with the CMB anisotropies

Early dark energy (EDE) models have attracted attention in the context of the recent problem of the Hubble tension. Here we extend these models by taking into account the new density fluctuations generated by the EDE which decays around the recombination phase.We solve the evolution of the density perturbations in dark energy fluid generated at the phase transition of EDE as isocurvature perturbations. Assuming that the isocurvature mode is characterized by a power-law power spectrum and is uncorrelated with the standard adiabatic mode, we calculate the CMB angular power spectra. By comparing them to the Planck data using the Markov-Chain Monte Carlo method, we obtained zero-consistent values of the EDE parameters and H 0 = 67.56+0.65 -0.66 km s-1 Mpc-1 at 68 % CL. This H 0 value is almost the same as the Planck value in the ΛCDM model, H 0 = 67.36 ± 0.54 km s-1 Mpc-1, and there is still a ∼ 3.5σ tension between the CMB and Type Ia supernovae observations. Including CMB lensing, BAO, supernovae and SH0ES data sets, we find H 0 = 68.94+0.47 -0.57 km s-1 Mpc-1 at 68 % CL. The amplitude of the fluctuations induced by the phase transition of the EDE is constrained to be less than 1–2 percent of the amplitude of the adiabatic mode. This is so small that such non-standard fluctuations cannot appear in the CMB angular spectra.In conclusion, the isocurvature fluctuations induced by our simplest EDE phase transition model do not explain the Hubble tension well.

Modified Starobinsky inflation by the R ln (□) R term

In the context of effective theories of gravity, a minimalist bottom-up approach which takes into account 1-loop quantum corrections leads to modifications in the Einstein-Hilbert action through the inclusion of four extra terms: R 2, CκραβCκραβ , R ln (□) R and Cκραβ ln(□) Cκραβ . The first two terms are necessary to guarantee the renormalizability of the gravitational theory, and the last two terms (nonlocal terms) arise from the integration of massless/light matter fields. This work aims to analyze how one of the nonlocal terms, namely R ln(□) R, affects the Starobinsky inflation. We consider the nonlocal term as a small correction to the R 2 term, and we demonstrate that the model behaves like a local model in this context. In addition, we show that the approximate model in the Einstein frame is described by a canonical scalar field minimally coupled to general relativity. Finally, we study the inflationary regime of this model and constrain its free parameters through observations of CMB anisotropies.

Constraining spatial curvature with large-scale structure

We analyse the clustering of matter on large scales in an extension of the concordance model that allows for spatial curvature. We develop a consistent approach to curvature and wide-angle effects on the galaxy 2-point correlation function in redshift space. In particular we derive the Alcock-Paczynski distortion of fσ 8, which differs significantly from empirical models in the literature. A key innovation is the use of the 'Clustering Ratio', which probes clustering in a different way to redshift-space distortions, so that their combination delivers more powerful cosmological constraints. We use this combination to constrain cosmological parameters, without CMB information. In a curved Universe, we find that Ωm, 0=0.26± 0.04 (68% CL). When the clustering probes are combined with low-redshift background probes — BAO and SNIa — we obtain a CMB-independent constraint on curvature: Ω K, 0 = 0.0041-0.0504 +0.0500. We find no Bayesian evidence that the flat concordance model can be rejected. In addition we show that the sound horizon at decoupling is r d = 144.57 ± 2.34 Mpc, in agreement with its measurement from CMB anisotropies. As a consequence, the late-time Universe is compatible with flat ΛCDM and a standard sound horizon, leading to a small value of H 0, without assuming any CMB information. Clustering Ratio measurements produce the only low-redshift clustering data set that is not in disagreement with the CMB, and combining the two data sets we obtain Ω K, 0 = -0.023 ± 0.010.

Modifications of CMB spectrum by nonextensive statistical mechanics

Cosmic microwave background radiation can supply us some most significant parts of the information on the universe. Some researchers believe that the gravitational system cannot be decribed by the standard statistical mechanics. In this article we apply Tsallis nonextensive statistical mechanics to investigate CMB spectrum and related cosmological processes. Based on recent observational data we find that the nonextensive statistical mechanics can modify the values of related physical quantities. Since the value of physical quantites have changed, some processes, such as recombination, can be affected. We have investigated the anisotropy of the CMB for two effects: the dipole anisotropy of CMB and the Sunyaev-Zel’dovich effect. We find that the dipole anisotropy of CMB cannot be modified by the nonextensive statistical mechanics. However, the standard result of the Sunyaev-Zel’sdovich effect should be modified by nonextensive statistical mechanics. In principle, future work can distinguish these effects.

Constant-roll inflation from a fermionic field

We study the inflationary period driven by a fermionic field which is non-minimally coupled to gravity in the context of the constant-roll approach. We consider the model for a specific form of coupling and perform the corresponding inflationary analysis. By comparing the result with the Planck observations coming from CMB anisotropies, we find the observational constraints on the parameters space of the model and also the predictions of the model. We find that the values of r and n s for are in good agreement with the observations when and N = 60.