Inflationary Power Spectrum Research Articles

Renormalization of the primordial inflationary power spectra

It has been suggested that the effects of renormalization significantly reduce the amplitude of the inflationary spectra at scales measurable in the cosmic microwave background. Via a gauge-invariant analysis, we compute the renormalized scalar and tensor power spectra and follow their evolution in an inflating universe that undergoes a transition to an FRW phase with a growing horizon. For perturbations originating from Minkowski vacuum fluctuations, we show that the standard prediction for the spectra on superhorizon scales is a late-time attractor, while they are UV finite at all times. Our result is independent of the equation of state after inflation, showing that the standard prediction is fully robust.

Primordial black hole production in natural and hilltop inflation

We consider the possibility of primordial black hole, PBH, formation sourced by a rise in the power spectrum. The power spectrum becomes large at late times due to decay of the inflaton into vectors through a ϕFF̃ coupling. Two background inflaton models which are well supported by current Planck data are considered, natural inflation and hilltop inflation. Many of the papers considering formation of PBHs have considered a peaked power spectrum where Pζ gets small again at late times. This avoids overproducing miniature PBHs which would evaporate and could violate BBN and CMB bounds. This paper examines the other way of avoiding these bounds, producing PBHs from perturbations formed closer to the end of inflation such that the PBHs are too small to violate these bounds. This has the advantage of allowing for simpler models in that no additional feature is needed to be added to evade constraints. Although these black holes would have evaporated, they can be close to without exceeding current BBN bounds, making it possible the signature will be revealed in the future. We calculate how the various model parameters affect the mass and number of PBHs produced. Any evidence for PBHs sourced from an inflationary power spectrum would provide evidence for inflation on a drastically different energy scale from the CMB, and thus would be highly valuable in answering what occurred during inflation.

Observational assessment of the viability of de Sitter Gödel de Sitter phase transition

de Sitter--G\"odel--de Sitter phase transition(dGd) is a possible geometrical phase transition in the very early universe. It induces fluctuations with possibly observable traces on matter and radiation fields. Here we present a simulation based on dGd to investigate possible perturbations which could be along with the standard inflationary fluctuations in the cosmic microwave background (CMB) and distribution of the large-scale structure. The power spectrum of perturbations is characterized by a parameter pair, labeled here as ($p_1, p_2$). With {\it Planck} observations we find $p_1=0.008^{+0.003}_{-0.008}$ and $p_2= 0.002^{+0.001}_{-0.002}$ consistent with pure inflationary power spectrum and no hint for the dGd transition. Also, it is estimated future large-scale surveys such as Euclid and SKA can further tighten the constraints up to an order of magnitude and probe the physics of the early universe with much higher precision.

Investigating the constraints on primordial features with future cosmic microwave background and galaxy surveys

In this article, we do a thorough investigation of the competency of the forthcoming Cosmic Microwave Background (CMB) and Galaxy surveys in probing the features in the primordial power spectrum. Primordial features are specific model-dependent corrections on top of the standard power-law inflationary power spectrum; the functional form being given by different inflationary scenarios. Signature of any significant departure from the feature-less power spectrum will enable us to decipher the intricacies of the inflationary Universe. Here, we delve into three major yet distinct features, namely, Bump feature, Sharp feature signal, and Resonance feature signal. To analyse the features, we adopt a specific template for each feature model. We estimate the possible constraints on the feature parameters by employing Fisher matrix forecast analysis for the upcoming CMB missions such as CMB-S4, CORE-M5, LiteBIRD, PICO conjointly with DESI, and EUCLID galaxy surveys. To this end, we make use of four distinct observations to forecast on the bounds on the model parameters, namely, CMB, Baryon Acoustic Oscillations (BAO), Galaxy Clustering and Gravitational Weak Lensing orCosmic Shear and their permissible synergy. For large scale structure (LSS) information, we consider different upper limits of scale for different redshifts for the purpose of circumventing the propagation of the errors stemming from the uncertainties on nonlinear scales into the constraints on the feature parameters. A comparative analysis of all three features has been done to estimate relative capabilities of these upcoming observations in shedding light on this crucial aspect of precision cosmology.

Formation and Abundance of Late-forming Primordial Black Holes as Dark Matter

We propose a novel mechanism where primordial black hole (PBH) dark matter is formed much later in the history of the universe, between the epochs of Big Bang nucleosynthesis and cosmic microwave background photon decoupling. In our setup, one does not need to modify the scale-invariant inflationary power spectra; instead, a late-phase transition in a strongly interacting fermion–scalar fluid (which occurs naturally around redshift 106 ≤ z T ≤ 108) creates an instability in the density perturbation as the sound speed turns imaginary. As a result, the dark matter perturbation grows exponentially in sub-Compton scales. This follows the immediate formation of an early dense dark matter halo, which finally evolves into PBHs due to cooling through scalar radiation. We calculate the variance of the density perturbations and the PBH fractional abundances f(M) by using a nonmonochromatic mass function. We find that the peak of our PBH mass function lies between 10−16 and 10−14 solar mass for z T ≃ 106, and thus that it can constitute the entire dark matter of the universe. In PBH formation, one would expect a temporary phase where an attractive scalar balances the Fermi pressure. We numerically confirm that such a state indeed exists, and we find the radius and density profile of the temporary static structure of the dark matter halo, which finally evolves into PBHs due to cooling through scalar radiation.

Scalaron\u2013Higgs inflation reloaded: Higgs-dependent scalaron mass and primordial black hole dark matter

We propose an extension of the scalaron-Higgs model by a non-minimal coupling of the Standard Model Higgs boson to the quadratic Ricci scalar resulting in a Higgs-dependent scalaron mass. The model predicts a successful stage of effective single-field Starobinsky inflation. It features a multi-field amplification mechanism leading to a peak in the inflationary power spectrum at small wavelengths which enhances the production of primordial black holes. The extended scalaron-Higgs model unifies inflationary cosmology with elementary particle physics and explains the origin of cold dark matter in terms of primordial black holes without assuming any new particles.

Primordial black hole dark matter in dilaton-extended two-field Starobinsky inflation

We investigate the production of primordial black holes and their contribution to the presently observed dark matter in a dilaton two-field extension of Starobinsky's quadratic $f(R)$ model of inflation. The model features a multi-field amplification mechanism which leads to the generation of a sharp peak in the inflationary power spectrum at small wavelengths responsible for the production of primordial black holes. This mechanism is significantly different from single-field models and requires a stochastic treatment during an intermediate phase of the inflationary dynamics. We find that the model leads to a successful phase of effective single-field Starobinsky inflation for wavelengths probed by the cosmic microwave background radiation and explains the observed cold dark matter content in the Universe by the formation of primordial black holes.

Scalaron-Higgs inflation

In scalaron-Higgs inflation the Standard Model Higgs boson is non-minimally coupled to gravity and the Einstein-Hilbert action is supplemented by the quadratic scalar curvature invariant. For the quartic Higgs self-coupling λ fixed at the electroweak scale, we find that the resulting inflationary two-field model effectively reduces to a single field model with the same predictions as in Higgs inflation or Starobinsky inflation, including the limit of a vanishing non-minimal coupling. For the same model, but with the scalar field a priori not identified with the Standard Model Higgs boson, we study the inflationary consequences of an extremely small λ. Depending on the initial conditions for the inflationary background trajectories, we find that the two-field dynamics either again reduces to an effective single-field model with a larger tensor-to-scalar ratio than predicted in Higgs inflation and Starobinsky inflation, or involves the full two-field dynamics and leads to oscillatory features in the inflationary power spectrum. Finally, we investigate under which conditions the inflationary scenario with extremely small λ can be realized dynamically by the Standard Model renormalization group flow and discuss how the scalaron-Higgs model can provide a natural way to stabilize the electroweak vacuum.

Lighting the Dark: Evolution of the Postinflationary Universe.

In simple inflationary cosmological scenarios, the near-exponential growth can be followed by a long period in which the Universe is dominated by the oscillating inflaton condensate. The condensate is initially almost homogeneous, but perturbations grow gravitationally, eventually fragmenting the condensate if it is not disrupted more quickly by resonance or prompt reheating. We show that the gravitational fragmentation of the condensate is well-described by the Schrödinger-Poisson equations and use numerical solutions to show that large overdensities form quickly after the onset of nonlinearity. This is the first exploration of this phase of nonlinear dynamics in the very early Universe, which can affect the detailed form of the inflationary power spectrum and the dark matter fraction when the dark sector is directly coupled to the inflaton.

Threshold for primordial black holes: Dependence on the shape of the cosmological perturbations

Primordial black holes may have formed in the radiative era of the early Universe from the collapse of large enough amplitude perturbations of the metric. These correspond to non linear energy density perturbations characterized by an amplitude larger than a certain threshold, measured when the perturbations reenter the cosmological horizon. The process of primordial black hole formation is studied here within spherical symmetry, using the gradient expansion approximation in the long wavelength limit, where the pressure gradients are small, and the initial perturbations are functions only of a time-independent curvature profile. In this regime it is possible to understand how the threshold for primordial black hole formation depends on the shape of the initial energy density profile, clarifying the relation between local and averaged measures of the perturbation amplitude. Although there is no universal threshold for primordial black hole formation, the averaged mass excess of the perturbation depends on the amplitude of the energy density peak, and it is possible to formulate a well-defined criterion to establish when a cosmological perturbation is able to form a black hole in terms of one of these two key quantities. This gives understanding of how the abundance of primordial black holes depends on the shape of the the inflationary power spectrum of cosmological perturbations.

Quantum gravitational corrections to the inflationary power spectra in scalar–tensor theories

We derive the first quantum gravitational corrections to the inflationary power spectra for a general single-field scalar–tensor theory which includes a non-minimal coupling to gravity, a non-standard scalar kinetic term and an arbitrary potential of the scalar field. We obtain these corrections from a semiclassical expansion of the Wheeler–DeWitt equation, which, in turn, governs the full quantum dynamics in the canonical approach to quantum gravity. We discuss the magnitude and relevance of these corrections, as well as their characteristic signature in the inflationary spectral observables. We compare our results to similar calculations performed for a minimally coupled scalar field with a canonical kinetic term and discuss the impact of the non-minimal coupling on the quantum gravitational corrections.

Observational constraints on warm inflation in loop quantum cosmology

By incorporating quantum aspects of gravity, Loop Quantum Cosmology (LQC) provides a self-consistent extension of the inflationary scenario, allowing for modifications in the primordial inflationary power spectrum with respect to the standard General Relativity one. We investigate such modifications and explore the constraints imposed by the Cosmic Microwave Background (CMB) Planck Collaboration data on the Warm Inflation (WI) scenario in the LQC context. We obtain useful relations between the dissipative parameter of WI and the bounce scale parameter of LQC. We also find that the number of required e-folds of expansion from the bounce instant till the moment the observable scales crossed the Hubble radius during inflation can be smaller in WI than in CI. In particular, we find that this depends on how large is the dissipation in WI, with the amount of required e-folds decreasing with the increasing of the dissipation value. {}Furthermore, by performing a Monte Carlo Markov Chain analysis for the considered WI models, we find good agreement of the model with the data. This shows that the WI models studied here can explain the current observations also in the context of LQC.

Primordial black holes with multimodal mass spectra

A mechanism for generating primordial black-hole mass spectra with many spikes is proposed and investigated. This mechanism relies on the choice of non-Bunch-Davies vacua, these leading to oscillatory features in the inflationary power spectrum. This in turn generates oscillations in the primordial black-hole mass function with exponentially enhanced spikes. This ``multimodal'' effect is demonstrated for most of the well-studied models of primordial black-hole formation.

Abundance of Primordial Black Holes Depends on the Shape of the Inflationary Power Spectrum.

In this Letter, combining peak theory and the numerical analysis of gravitational collapse in the radiation dominated era, we show that the abundance of primordial blacks holes, generated by an enhancement in the inflationary power spectrum, is extremely dependent on the shape of the peak. Given the amplitude of the power spectrum, we show that the density of primordial black holes generated from a narrow peak is exponentially smaller than in the case of a broad peak. Specifically, for a top-hat profile of the power spectrum in Fourier space, we find that to have primordial black holes comprising all of the dark matter, one would only need a power spectrum amplitude an order of magnitude smaller than suggested previously, whereas in the case of a narrow peak, one would instead need a much larger power spectrum amplitude, which in many cases would invalidate the perturbative analysis of cosmological perturbations. Finally, we show that, although critical collapse gives a broad mass spectrum, the density of primordial black holes formed is dominated by masses roughly equal to the cosmological horizon mass measured at horizon crossing.

Molecular Ionization Rates and Ultracompact Dark Matter Minihalos.

Molecular ionization in the central molecular zone of our Galaxy is enhanced over the typical galactic value by an order of magnitude or more. This cannot be easily explained for dense Galactic center molecular complexes in the absence of embedded sources of low energy cosmic rays. We provide such a source in the form of ultracompact minihalos of self-annihilating dark matter for a variety of annihilation channels that depend on the particle mass and model. Such sources are motivated for plausible inflationary power spectrum parameters, and while possibly subdominant in terms of the total dark matter mass within the Galactic bulge, might also account for, or at least not be in tension with, the Fermi Galactic center γ-ray excess.

Connecting CMB anisotropy and cold dark matter phenomenology via reheating

Understanding the properties of dark matter has proved to be one of the most challenging problems of particle phenomenology. In this paper, we have tried to understand the phenomenology of dark matter in light of very well understood properties of cosmic microwave background (CMB) anisotropy. To connect these two, inflation and its subsequent evolution known as the reheating phase play the important role. Following the previous analysis, we first established a one-to-one correspondence between the CMB power spectrum and the reheating temperature assuming the perturbative reheating scenario. Further by incorporating a possible dark matter candidate through the radiation annihilation process during reheating and the current value of dark matter abundance, we constrain the dark matter parameter space through the inflationary power spectrum for different inflationary models.

Inflationary versus reionization features from Planck 2015 data

Features during inflation and reionization leave corresponding features in the temperature and polarization power spectra that could potentially explain anomalies in the Planck 2015 data but require a joint analysis to disentangle. We study the interplay between these two effects using a model-independent parametrization of the inflationary power spectrum and the ionization history. Preference for a sharp suppression of large-scale power is driven by a feature in the temperature power spectrum at multipoles $\ensuremath{\ell}\ensuremath{\sim}20$, whereas preference for a component of high redshift ionization is driven by a sharp excess of polarization power at $\ensuremath{\ell}\ensuremath{\sim}10$ when compared with the lowest multipoles. Marginalizing inflationary freedom does not weaken the preference for $z\ensuremath{\gtrsim}10$ ionization, whereas marginalizing reionization freedom slightly enhances the preference for an inflationary feature but can also mask its direct signature in polarization. The inflation and reionization interpretation of these features makes predictions for the polarization spectrum which can be tested in future precision measurements especially at $10\ensuremath{\lesssim}\ensuremath{\ell}\ensuremath{\lesssim}40$.

Anomaly free cosmological perturbations with generalised holonomy correction in loop quantum cosmology

In the spatially flat case of loop quantum cosmology, the connection is usually replaced by the holonomy in effective theory. In this paper, instead of the standard scheme, we use a generalised, undetermined function to represent the holonomy and by using the approach of anomaly free constraint algebra we fix all the counter terms in the constraints and find the restriction in the form of , then we derive the gauge-invariant equations of motion of the scalar, tensor and vector perturbations and study the inflationary power spectra with generalised holonomy correction.

Uncertainties in primordial black-hole constraints on the primordial power spectrum

The existence (and abundance) of primordial black holes (PBHs) is governed by the power spectrum of primordial perturbations generated during inflation. So far no PBHs have been observed, and instead, increasingly stringent bounds on their existence at different scales have been obtained. Up until recently, this has been exploited in attempts to constrain parts of the inflationary power spectrum that are unconstrained by cosmological observations. We first point out that the simple translation of the PBH non-observation bounds into constraints on the primordial power spectrum is inaccurate as it fails to include realistic aspects of PBH formation and evolution. We then demonstrate, by studying two examples of uncertainties from the effects of critical and non-spherical collapse, that even though they may seem small, they have important implications for the usefulness of the constraints. In particular, we point out that the uncertainty induced by non-spherical collapse may be much larger than the difference between particular bounds from PBH non-observations and the general maximum cap stemming from the condition $\Omega \leq 1$ on the dark-matter density in the form of PBHs. We therefore make the cautious suggestion of applying only the overall maximum dark-matter constraint to models of early Universe, as this requirement seems to currently provide a more reliable constraint, which better reflects our current lack of detailed knowledge of PBH formation. These, and other effects, such as merging, clustering and accretion, may also loosen constraints from non-observations of other primordial compact objects such as ultra-compact minihalos of dark matter.

Detecting higher spin fields through statistical anisotropy in the CMB and galaxy power spectra

Primordial inflation may represent the most powerful collider to test high-energy physics models. In this paper we study the impact on the inflationary power spectrum of the comoving curvature perturbation in the specific model where massive higher spin fields are rendered effectively massless during a de Sitter epoch through suitable couplings to the inflaton field. In particular, we show that such fields with spin $s$ induce a distinctive statistical anisotropic signal on the power spectrum, in such a way that not only the usual ${g}_{2M}$-statistical anisotropy coefficients, but also higher-order ones (i.e., ${g}_{4M},{g}_{6M},\dots{},{g}_{(2s\ensuremath{-}2)M}$ and ${g}_{(2s)M}$) are nonvanishing. We examine their imprints in the cosmic microwave background and galaxy power spectra. Our Fisher matrix forecasts indicate that the detectability of ${g}_{LM}$ depends very weakly on $L$: all coefficients could be detected in near future if their magnitudes are bigger than about ${10}^{\ensuremath{-}3}$.