Scalar Spectral Index Research Articles

Unlocking the synergy between CMB spectral distortions and anisotropies

Measurements of the cosmic microwave background (CMB) spectral distortions (SDs) will open a new window on the very early universe, providing new information complementary to that gathered from CMB temperature and polarization anisotropies. In this paper, we study their synergy as a function of the characteristics of the considered experiments. In particular, we examine a wide range of sensitivities for possible SD measurements, spanning from FIRAS up to noise levels 1000 times better than PIXIE, and study their constraining power when combined with current or future CMB anisotropy experiments such as Planck or LiteBIRD plus CMB-S4. We consider a number of different cosmological models such as the ΛCDM, as well as its extensions with the running of the scalar spectral index, the decay or the annihilation of dark matter (DM) particles. While upcoming CMB anisotropy experiments will be able to decrease the uncertainties on inflationary parameters such as As and ns by about a factor 2 in the ΛCDM case, we find that an SD experiment 100 times more sensitive than PIXIE (comparable to the proposed Super-PIXIE satellite) could potentially further contribute to constrain these parameters. This is even more significant in the case of the running of the scalar spectral index. Furthermore, as expected, constraints on DM particles decaying at redshifts probed by SDs will improve by orders of magnitude even with an experiment 10 times worse than PIXIE as compared to CMB anisotropies or Big Bang Nucleosynthesis bounds. On the contrary, DM annihilation constraints will not significantly improve over CMB anisotropy measurements. Finally, we forecast the constraints obtainable with sensitivities achievable either from the ground or from a balloon.

Cosmological constraints on slow roll inflation: An update

In light of the most recent cosmological observations, we provide new updated constraints on the slow roll inflation in different extended scenarios beyond the $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ cosmological model. Along with the usual six parameters, we simultaneously vary different combinations of additional parameters, including the running of the scalar spectral index ${\ensuremath{\alpha}}_{s}$, its running of running ${\ensuremath{\beta}}_{s}$, the tensor amplitude $r$ and the spatial curvature ${\mathrm{\ensuremath{\Omega}}}_{k}$. From the Planck 2018 data, we find no evidence for a scalar running or a running of running, while analyzing the Atacama Cosmology Telescope data combined with WMAP 9-years observations data we find a preference for nonzero ${\ensuremath{\alpha}}_{s}$ and ${\ensuremath{\beta}}_{s}$ at the level of $2.9\ensuremath{\sigma}$ and $2.7\ensuremath{\sigma}$, respectively. Anyway, this preference is reduced when the tensor amplitude can vary in the model or ${\ensuremath{\beta}}_{s}$ is fixed to zero. The upper bound on $r$ is only slightly affected by the additional parameters while the differences in the datasets can remarkably change the compatibility among the different inflationary models, sometimes leading to discordant conclusions.

Sneutrino tribrid inflation, metastable cosmic strings and gravitational waves

We present a successful realization of sneutrino tribrid inflation model based on a gauged U(1)_B-L extension of Minimal Supersymmetric Standard Model (MSSM). A single interaction term involving the B-L Higgs field and the right-handed neutrinos serves multiple purposes. These include the generation of heavy Majorana masses for the right-handed neutrinos to provide an explanation for the tiny neutrino masses via the seesaw mechanism, a realistic scenario for reheating and non-thermal leptogenesis with a reheat temperature as low as 106 GeV, and a successful realization of inflation with right-handed sneutrino as the inflaton. The matter parity which helps avoid rapid proton decay survives as a Z2 subgroup of a U(1) R-symmetry. Depending on the choice of model parameters yields the following predicted range of the tensor to scalar ratio, 3 × 10-11≲ r≲ 7× 10-4 (6 × 10-7≲ r ≲ 0.01), and the running of the scalar spectral index, -0.00022 ≲ dn_s/dln k ≲ -0.0026 (-0.00014 ≲ dn_s/dln k ≲ 0.005), along with the B-L breaking scale, 3 × 1014≲ M/ GeV≲ 5 × 1015 (6 × 1015≲ M/ GeV≲ 2 × 1016), calculated at the central value of the scalar spectral index, n_s =0.966, reported by Planck 2018. The possibility of realizing metastable cosmic strings in a grand unified theory setup is briefly discussed. The metastable cosmic string network admits string tension values in the range 10-8≲ Gμs ≲ 10-6, and predicts a stochastic gravitational wave background lying within the 2-σ bounds of the recent NANOGrav 12.5-yr data.

Testing an inflationary era in curvature–matter coupling gravity

In this paper, we investigate the cosmological inflation in the context of a minimal matter–geometry coupling, which is based on the [Formula: see text] gravity theory, where [Formula: see text] is a generic function of the curvature scalar [Formula: see text] and the trace [Formula: see text] of the energy–momentum tensor. Assuming that the slow-roll inflation conditions hold true in [Formula: see text] gravity, we obtain the various inflation-related observables such as the tensor-to-scalar ratio [Formula: see text], the scalar spectral index [Formula: see text], the running [Formula: see text] of the spectral index and the tensor spectral [Formula: see text] for two specific [Formula: see text] models from the Hubble slow-roll parameters. To observe the viability of these models, a numerical analysis of such parameters has been done. The results showed that, by using the various values of free parameters, it is possible to obtain a viable compatible with the observational data.

Warm constant-roll inflation in brane-world cosmology

In this paper, we study a constant-roll inflationary model in the context of brane-world cosmology caused by a quintessence scalar field for warm inflation with a constant dissipative parameter [Formula: see text]. We determine the analytical solution for the Friedmann equation coupled to the equation of motion of the scalar field. The evolution of the primordial scalar and tensor perturbations is also studied using the modified Langevin equation. To check the viability of the model, we use numerical approaches and plot some figures. Our results for the scalar spectral index and the tensor-to-scalar ratio show good consistency with observations.

Realistic inflation in no-scale U(1) R symmetric flipped SU(5)

We have realized non-minimal Higgs inflation and standard hybrid inflation in the supersymmetric flipped SU(5) model with U(1) R symmetry using the no-scale form of the Kähler potential. In non-minimal Higgs inflation the waterfall Higgs field plays the role of inflaton, and in standard hybrid inflation the gauge singlet field S is employed as an inflaton. The predictions of both models are in good agreement with the Planck 2018 data. For numerical calculations we have fixed the gauge symmetry breaking scale, M, around 2 × 1016 GeV. In both models the inflaton field values are constrained below mP . The tensor to scalar ratio r in non-minimal inflation is of the order of 10-3 and for standard hybrid inflation r is tiny, of order 10-15–10-4. The scalar spectral index in both cases lie within the Planck 1-σ bounds, and the running of the scalar spectral index lies in the range, -dns /d ln k ∼ 6 × 10-4 for non-minimal model and 10-9–10-3 for the standard hybrid model. A realistic scenario of reheating and non-thermal leptogenesis is employed with reheat temperature Tr ∼ 109 GeV for non-minimal model and 106–1010 GeV for standard hybrid model. The R-symmetry plays a vital role in forbidding rapid proton decay, but at the same time it also suppresses terms responsible for generating right handed neutrino masses. A realistic scenario of right handed neutrino masses is obtained by considering effective R symmetry breaking at the nonrenormalizable level with adequate suppression of rapid proton decay.

Inflationary cosmology in [formula omitted] modified gravity

In this paper, we investigate the cosmological inflation scenario in the context of f(R,T) theory of gravity, where f is a generic function of the curvature scalar R and the trace T of the energy momentum tensor. Assuming that the slow roll inflation conditions hold true in f(R,T) gravity, we obtain from the Hubble slow roll parameters, the various inflation-related observables such as the tensor-to-scalar ratio r, the scalar spectral index ns, the running αs of the spectral index and the tensor spectral nT for two specific f(R,T) models. To see the viability of these models, a numerical analysis of such parameters has been done. The results show that by using the various values of free parameters it is possible to obtain a viable compatibility with the observational data.

A refined Einstein–Gauss–Bonnet inflationary theoretical framework

We provide a refined and much more simplified Einstein–Gauss–Bonnet inflationary theoretical framework, which is compatible with the GW170817 observational constraints on the gravitational wave speed. As in previous works, the constraint that the gravitational wave speed is in natural units, results to a constraint differential equation that relates the coupling function of the scalar field to the Gauss–Bonnet invariant ξ(ϕ) and the scalar potential V(ϕ). Adopting the slow-roll conditions for the scalar field and the Hubble rate, and in contrast to previous works, by further assuming that , which is motivated by slow-roll arguments, we succeed in providing much more simpler expressions for the slow-roll indices and for the tensor and scalar spectral indices and for the tensor-to-scalar ratio. We exemplify our refined theoretical framework by using an illustrative example with a simple power-law scalar coupling function ξ(ϕ) ∼ ϕ ν and as we demonstrate the resulting inflationary phenomenology is compatible with the latest Planck data. Moreover, this particular model produces a blue-tilted tensor spectral index, so we discuss in brief the perspective of describing the NANOGrav result with this model as is indicated in the recent literature.

Adiabatic duality: Duality of cosmological models with varying slow-roll parameter and sound speed

There have been thousands of cosmological models for our early universe proposed in the literature, and many of them claimed to be able to give rise to scale-invariant power spectrum as was favored by the observational data. It is thus interesting to think about whether there are some relations among them, e.g., the duality relation. In this paper, we investigate duality relations between cosmological models in framework of general relativity (GR) , not only with varying slow-roll parameter $\epsilon$, but also with sound speed $c_s$, which can then be understood as "adiabatic duality". Several duality relationships are formulated analytically and verified numerically. We show that models with varying $\epsilon$ and constant $c_s$ can be dual in scalar spectral index, but not tensor one. On the other hand, allowing both $\epsilon$ and $c_s$ to vary can make models dual in both scalar and tensor spectral indices.

Implication of the Hubble tension for the primordial Universe in light of recent cosmological data

In prerecombination resolutions of the Hubble tension, such as early dark energy, new physics before recombination shifts the values of relevant cosmological parameters so that the models can fit with cosmic microwave background and baryon acoustic oscillations observations as well as $\Lambda$CDM does. In this paper, we clarify how the parameter shifts are related with $\delta H_0$, particularly we find the shift of primordial scalar spectral index scales as ${\delta n_s}\simeq 0.4{\delta H_0\over H_0}$ by performing the Monte Carlo Markov chain analysis with the Planck2018+BAO+Pantheon+R19+Keck Array/BICEP dataset. A novel point of our result is that if the current $H_0$ measured locally is correct, complete resolution of the Hubble tension seems to be pointing to a scale invariant Harrison-Zeldovich spectrum, i.e. $n_s= 1$ for $H_0\sim 73$km/s/Mpc.

Inflation with R (αβ) terms in the Palatini formulation

We study inflation with the most general non-degenerate gravitational action that depends on the symmetric part of the Ricci tensor coupled to a scalar field in the Palatini formulation of gravity. We use field redefinitions to shift the effect of the Ricci terms from gravity to the scalar field, and apply the result to slow-roll inflation.As examples, we consider actions quadratic and cubic in the Ricci tensor. In the quadratic case the results are similar to the case R + α R 2 that has been studied earlier: the tensor-to-scalar ratio r can be suppressed by an arbitrary amount, while the scalar spectrum is unaffected. In the cubic case, r can be suppressed by at most a factor of 2/9, and the change in the scalar spectral index n s can be large.

On the α-attractor T-models

We carry out a fully analytical study of the phenomenology of α-attractor T-models defined by the potential V = V0tanhp(λϕ/M_pl). We obtain expressions for the number of e-folds during inflation Nke in terms of the scalar spectral index ns and independently in terms of the tensor-to-scalar ratio r. From these expressions we obtain exact solutions for both ns and r in terms of Nke along with their expansions for large Nke, in full agreement with known expressions. Eliminating the parameter λ from the model in terms of ns and r we can obtain exact solutions for r in terms of ns and Nke which allows us to reproduce, in particular, numerical solutions presented by the Planck Collaboration for the monomial potentials. We explicitly show how these solutions are contained in the solutions for the α-attractors and are also the end points of these. Finally, by also eliminating the global scale V0 in terms of the observables ns and r we show how in the appropriate limit the α-attractor potential exactly reduces to the monomials potential. We also briefly show that for α-attractor E-models, which generalize the Starobinsky potential in the Einstein frame, a similar transition occurs.

Viable intermediate inflation in the mimetic DBI model

We study the intermediate inflation in the mimetic Dirac–Born–Infeld model. By considering the scale factor as a=a_{0}exp (bt^{beta }), we show that in some ranges of the intermediate parameters b and beta , the model is free of the ghost and gradient instabilities. We study the scalar spectral index, tensor spectral index, and the tensor-to-scalar ratio in this model and compare the results with Planck2018 TT, TE, EE + lowE + lensing + BAO + BK14 data at 68% and 95% CL. In this regard, we find some constraints on the intermediate parameters that lead to the observationally viable values of the perturbation parameters. We also seek the non-Gaussian features of the primordial perturbations in the equilateral configuration. By performing the numerical analysis on the nonlinearity parameter in this configuration, we show that the amplitude of the non-Gaussianity in the intermediate mimetic DBI model is predicted to be in the range -16.7<f^{equil}<-12.5. We show that, with 0<ble 10 and 0.345<beta <0.387, we have an instabilities-free intermediate mimetic DBI model that gives the observationally viable perturbation and non-Gaussianity parameters.

Extracting cosmological parameters from N-body simulations using machine learning techniques

We make use of snapshots taken from the Quijote suite of simulations, consisting of 2000 simulations where five cosmological parameters have been varied (Ωm, Ωb, h, n s and σ8) in order to investigate the possibility of determining them using machine learning techniques. In particular, we show that convolutional neural networks can be employed to accurately extract Ω m and σ 8 from the N-body simulations, and that these parameters can also be found from the non-linear matter power spectrum obtained from the same suite of simulations using both random forest regressors and deep neural networks. We show that the power spectrum provides competitive results in terms of accuracy compared to using the simulations and that we can also estimate the scalar spectral index n s from the power spectrum, at a lower precision.

Attractor and slow roll parameterized inflation in extended teleparallel gravity

The study of inflation through different prospects is being done for specific model of scalar f(T) gravity in two phases such as attractor (ns(N)−1∝N−1) and slow roll parameterizations. In the presence of these ingredients, we evaluate all inflationary parameters such as scalar spectral index, tensor to scalar ratio r and running of scalar spectral index and local non Gaussianity parameter. We also develop the inflationary planes ns−N, r−N, dnsdlnκ−N, dnsdlnκ−ns and fNL−ns. These planes show the viability of our outcomes with Planck data 2018.

Preheating and reheating constraints in supersymmetric braneworld inflation

We study the evolution of the Universe at early stages, we discuss also preheating in the framework of hybrid braneworld inflation by setting conditions on the coupling constants $\lambda $ and $g$\ for effective production of $\chi$-particles. Considering the phase between the time observable CMB scales crossed the horizon and the present time, we write reheating and preheating parameters $N_{re}$, $T_{re}$ and $N_{pre}$ in terms of the scalar spectral index $n_{s}$, and prove that, unlike the reheating case, the preheating duration does not depend on the values of the equation of state $\omega ^{\ast }$. We apply the slow-roll approximation in the high energy limit to constrain the parameters of D-term hybrid potential. We show also that some inflationary parameters, in particular, the spectral index $n_{s}$ demand that the potential parameter $\alpha$ is bounded as $\alpha \geq 1$ to be consistent with $Planck$'s data, while the ratio $r$ is in agreement with observation for $ \alpha \leq 1 $ considering high inflationary e-folds. We also propose an investigation of the brane tension effect on the reheating temperature. Comparing our results to recent CMB measurements, we study preheating and reheating parameters $N_{re}$, $T_{re}$ and $N_{pre}$ in the Hybrid D-term inflation model in the range $0.8\leq \alpha\leq 1.1$\, and conclude that $T_{re}$ and $N_{re}$ require $\alpha \leq 1$, while for $N_{pre}$ the condition $\alpha \leq 0.9$ must be satisfied, to be compatible with $Planck$'s results.

Reconstructing inflation in scalar-torsion f(T,phi ) gravity

It is investigated the reconstruction during the slow-roll inflation in the most general class of scalar-torsion theories whose Lagrangian density is an arbitrary function f(T,phi ) of the torsion scalar T of teleparallel gravity and the inflaton phi . For the class of theories with Lagrangian density f(T,phi )=-M_{pl}^{2} T/2 - G(T) F(phi ) - V(phi ), with G(T)sim T^{s+1} and the power s as constant, we consider a reconstruction scheme for determining both the non-minimal coupling function F(phi ) and the scalar potential V(phi ) through the parametrization (or attractor) of the scalar spectral index n_{s}(N) and the tensor-to-scalar ratio r(N) as functions of the number of e-folds N. As specific examples, we analyze the attractors n_{s}-1 propto 1/N and rpropto 1/N, as well as the case rpropto 1/N (N+gamma ) with gamma a dimensionless constant. In this sense and depending on the attractors considered, we obtain different expressions for the function F(phi ) and the potential V(phi ), as also the constraints on the parameters present in our model and its reconstruction.

Inflation with non-canonical scalar fields revisited

We revisit inflation with non-canonical scalar fields by applying deformed-steepness exponential potentials. We show that the resulting scenario can lead to inflationary observables, and in particular to scalar spectral index and tensor-to-scalar ratio, in remarkable agreement with observations. Additionally, a significant advantage of the scenario is that the required parameter values, such as the non-canonicality exponent and scale, as well as the potential exponent and scale, do not need to acquire unnatural values and hence can accept a theoretical justification. Hence, we obtain a significant improvement with respect to alternative schemes, and we present distinct correlations between the model parameters that better fit the data, which can be tested in future probes. This combination of observational efficiency and theoretical justification makes the scenario at hand a good candidate for the description of inflation.

Holographic inflation in f(T) and DGP braneworld

In this paper, we investigate the holographic inflation in the framework of two gravitational theories like [Formula: see text] gravity, where [Formula: see text] corresponds to the torsion scalar and DGP braneworld model which is based on the idea that our four-dimensional FRW universe located on five-dimensional manifold. The modified infrared cutoff is used to explore all the inflationary parameters as slow-roll parameters [Formula: see text], number of [Formula: see text]-folds [Formula: see text], scalar spectral index [Formula: see text], tensor-to-scalar ratio [Formula: see text] and running of the scalar spectral index [Formula: see text]. Also, we investigate the behavior of inflationary parameters [Formula: see text] and [Formula: see text] through graphical presentation. The behavior of these parameters shows the consistency with Planck data [Formula: see text].

Construction of inflationary scenarios with the Gauss\u2013Bonnet term and nonminimal coupling

Inflationary models with a scalar field nonminimally coupled both with the Ricci scalar and with the Gauss–Bonnet term are studied. We propose the way of generalization of inflationary scenarios with the Gauss–Bonnet term and a scalar field minimally coupled with the Ricci scalar to the corresponding scenarios with a scalar field nonminimally coupled with the Ricci scalar. Using the effective potential, we construct a set of models with the same values of the scalar spectral index n_s and the amplitude of the scalar perturbations A_s and different values of the tensor-to-scalar ratio r.