We explore possible constraints on the inflationary equation state: p=wρ. While w must be close to -1 for those modes that contribute to the observed power spectrum, for those modes currently out of experimental reach, the constraints on w are much weaker, with only w<-1/3 as an a priori requirement. We find, however, that limits on the reheat temperature and the inflationary energy scale constrain w further, though there is still ample parameter space for a vastly different (accelerating) equation of state between the end of quasi-de Sitter inflation and the beginning of the radiation-dominated era. In the event that such an epoch of acceleration could be observed, we review the consequences for the primordial power spectrum.
In this paper we constrain some aspects of the general postinflationary phase in the context of superconformal $α$-attractor models of inflation. In particular, we provide constraints on the duration of the reheating process, $N_{reh}$, and on the reheating temperature, $T_{reh}$, simulating possible and future results given by the next-generation of cosmological missions. Moreover, we stress what kinds of equation-of-state parameter, $w_{reh}$, are favored for different scenarios. The analysis does not depend on the details of the reheating phase and it is performed assuming different measure…
Inflationary cosmology is the leading explanation of the very early universe. Many different models of inflation have been constructed which fit current observational data. In this work theoretical and numerical methods for constraining the parameter space of a wide class of such models are described. First, string-theoretic models with large non-Gaussian signatures are investigated. An upper bound is placed on the amplitude of primordial gravitational waves produced by ultra-violet Dirac-Born-Infeld inflation. In all but the most finely tuned cases, this bound is incompatible with a lower bou…
In this paper we will illustrate how to constrain unavoidable Kähler corrections for ${\cal N}=1$ supergravity (SUGRA) inflation from the recent Planck data. We will show that the non-renormalizable Kähler operators will induce in general non-minimal kinetic term for the inflaton field, and two types of SUGRA corrections in the potential - the Hubble-induced mass ($c_{H}$), and the Hubble-induced A-term ($a_{H}$) correction. The entire SUGRA inflationary framework can now be constrained from (i) the speed of sound, $c_s$, and (ii) from the upper bound on the tensor to scalar ratio, $r_{\star}$…
If, after primordial inflation, the universe undergoes a relatively long reheating period, it could present a phase of matter domination supported by the oscillating inflaton field. During this epoch, small perturbations from the inflaton that reenter the cosmological horizon could virialize to form \textit{inflaton} structures. If the primordial overdensities are large enough, their associated inflaton structures could collapse to form primordial black holes (PBHs) [L.E.Padilla, J.C.Hidalgo and K.A.Malik, Phys.Rev.D, vol.106, p.023519, Jul 2022; hereinafter P1]. For this to happen at a consid…
Using renormalization-group flow and cosmological constraints on inflation models, we exploit a unique connection between cosmological inflation and the dynamical mass of dark-matter particles in the luminogenesis model, a unification model with the gauge group $SU(3)_C \times SU(6) \times U(1)_Y$, which breaks to the Standard Model with an extra gauge group for dark matter when the inflaton rolls into the true vacuum. In this model, inflaton decay gives rise to dark matter, which in turn decays to luminous matter in the right proportion that agrees with cosmological data. Some attractive feat…
In this article, I have studied the cosmological and particle physics constraints on a generic class of large field ($|Δϕ|>M_{p}$) and small field ($|Δϕ<M_{p}$) models of brane inflationary magnetic field from: (1) tensor-to-scalar ratio ($r$), (2) reheating, (3) leptogenesis and (4) baryogenesis in case of Randall-Sundrum single braneworld gravity (RSII) framework. I also establish a direct connection between the magnetic field at the present epoch ($B_{0}$) and primordial gravity waves ($r$), which give a precise estimate of non-vanishing CP asymmetry ($ε_{CP}$) in leptogenesis and baryon as…
The ability to test and constrain theories of cosmic inflation will advance substantially over the next decade. Key data sources include cosmic microwave background (CMB) measurements and observations of the distribution of matter at low-redshift from optical, near-infrared, and 21cm intensity surveys. A positive detection of a CMB B-mode consistent with a primordial stochastic gravitational wave background (SGWB) is widely viewed as a smoking gun for an inflationary phase. Still, a null result does not exclude inflation. However, in a significant class of inflationary scenarios, a low SGWB am…
The hypothesis of the self-induced collapse of the inflaton wave function was proposed as responsible for the emergence of inhomogeneity and anisotropy at all scales. This proposal was studied within an almost de Sitter space-time approximation for the background, which led to a perfect scale-invariant power spectrum, and also for a quasi-de Sitter background, which allows to distinguish departures from the standard approach due to the inclusion of the collapse hypothesis. In this work we perform a Bayesian model comparison for two different choices of the self-induced collapse in a full quasi…
Measuring spectral distortions (SDs) of the cosmic microwave background (CMB) will provide new constraints on previously unexplored scales of the primordial power spectrum, allowing us to extend the probed parameter space by several orders of magnitude in $k$-space, which could have significant implications in the context of primordial black holes and gravitational waves, among others. Here we discuss how various models of inflation can be tightly constrained by the combination of current and future CMB SD and anisotropy experiments. In particular, we investigate the constraining power of SD e…
Generation of magnetic field during inflation can explain its presence over a wide range of scales in the Universe. In Ref.\cite{sharma2017}, we proposed a model to generate these fields during inflation. These fields have nonzero anisotropic stress which lead to the generation of a stochastic background of gravitational waves (GW) in the early universe. Here we show that for a scenario of magnetogenesis where reheating takes place around QCD epoch, this stochastic GW background lies in the $95\%$ confidence region of the GW signal probed by NANOGrav collaboration. This is the case when the ge…
Constraining Inflationary Particle Production with CMB Polarization
Columbia University（哥伦比亚大学）；Leinweber Institute for Theoretical Physics at Stanford（斯坦福莱因韦伯理论物理研究所）；Kavli Institute for Particle Astrophysics and Cosmology（卡弗里粒子天体物理学与宇宙学研究所）；Simons Society of Fellows, Simons Foundation（西蒙斯基金会西蒙斯研究员协会）
The Cosmic Microwave Background can provide information regarding physics of the very early universe, more specifically, of the matter-radiation distribution of the inflationary era. Starting from the effective field theory of inflation, we use the Goldstone action to calculate the three point correlation function for the Goldstone field, whose results can be directly applied to the field describing the curvature perturbations around a de Sitter solution for the inflationary era. We then use the data from the recent Planck mission for the parameters $f_{NL}^{equil}$ and $f_{NL}^{orthog}$ which…
We present proof of principle for a two way interplay between physics at very early Universe and late time observations. We find a relation between primordial mechanisms responsible for large scale power suppression in the primordial power spectrum and the value of reionization optical depth $τ$. Such mechanisms can affect the estimation of $τ$. We show that using future measurements of $τ$, one can obtain constraints on the pre-inflationary dynamics, providing a new window on the physics of the very early Universe. Furthermore, the new, re-estimated $τ$ can potentially resolve moderate discre…
We revisit the predictions for the duration of the inflationary phase after the bounce in loop quantum cosmology. We present our analysis for different classes of inflationary potentials that include the monomial power-law chaotic type of potentials, the Starobinsky and the Higgs-like symmetry breaking potential with different values for the vacuum expectation value. Our setup can easily be extended to other forms of primordial potentials than the ones we have considered. Independently on the details of the contracting phase, if the dynamics starts sufficiently in the far past, the kinetic ene…
The hypothesis of the self-induced collapse of the inflaton wave function was introduced as a candidate for the physical process responsible for the emergence of inhomogeneity and anisotropy at all scales. In particular, we consider different proposal for the precise form of the dynamics of the inflaton wave function: i) the GRW-type collapse schemes proposals based on spontaneous individual collapses which generate non-vanishing expectation values of various physical quantities taken as ansatz modifications of the standard inflationary scenario; ii) the proposal based on a Continuous Spontane…
Constraining primordial oscillations and inflationary particle production with Planck, ACT DR6, and DESI DR2
David A. Dunlap Department of Astronomy & Astrophysics, University of Toronto（多伦多大学戴维·A·邓拉普天文学与天体物理学系）；Dunlap Institute for Astronomy and Astrophysics, University of Toronto（多伦多大学邓拉普天文学与天体物理学研究所）；School of Physics and Astronomy, Cardiff University（卡迪夫大学物理与天文学院）；Canadian Institute for Theoretical Astrophysics, University of Toronto（多伦多大学加拿大理论天体物理研究所）
In this short paper, we present constraints on the Galileon inflationary model from the CMB bispectrum. We employ a principal-component analysis of the independent degrees of freedom constrained by data and apply this to the WMAP 9-year data to constrain the free parameters of the model. A simple Bayesian comparison establishes that support for the Galileon model from bispectrum data is at best weak.
Constraining Quintessential Inflation with ACT: A Gauss-Bonnet Gateway
Institute for Theoretical Physics and Cosmology, Zhejiang University of Technology（浙江工业大学理论物理与宇宙学研究所）；Department of Physics, Islamic University of Science and Technology（伊斯兰科技大学物理系）；Department of Physics, School of Advanced Sciences, Vellore Institute of Technology (VIT)（维罗尔理工学院高级科学学院物理系）；Centre for Cosmology and Science Popularization (CCSP), SGT University（SGT大学宇宙学与科学普及中心）
We use transport techniques to calculate the trispectrum produced in multiple-field inflationary models with canonical kinetic terms. Our method allows the time evolution of the local trispectrum parameters, tauNL and gNL, to be tracked throughout the inflationary phase. We illustrate our approach using examples. We give a simplified method to calculate the superhorizon part of the relation between field fluctuations on spatially flat hypersurfaces and the curvature perturbation on uniform density slices, and obtain its third-order part for the first time. We clarify how the 'backwards' formal…
It is commonly assumed that the stochastic background of gravitational waves on cosmological scales follows an almost scale-independent power spectrum, as generically predicted by the inflationary paradigm. However, it is not inconceivable that the spectrum could have strongly scale-dependent features, generated, e.g., via transient dynamics of spectator axion-gauge fields during inflation. Using the temperature and polarisation maps from the \textit{Planck} and BICEP/Keck datasets, we search for such features, taking the example of a log-normal bump in the primordial tensor spectrum at CMB sc…
We present a simple and efficient method to compute the superhorizon evolution of the spectral index in multi-field inflationary models, using transport equation techniques. We illustrate the evolution of n_s with time for various interesting potentials.
In a previous paper, we connected the phenomenological non-commutative inflation of Alexander, Brandenberger and Magueijo (2003) and Koh S and Brandenberger (2007) with the formal representation theory of groups and algebras and analyzed minimal conditions that the deformed dispersion relation should satisfy in order to lead to a successful inflation. In that paper, we showed that elementary tools of algebra allow a group like procedure in which even Hopf algebras (roughly the symmetries of non-commutative spaces) could lead to the equation of state of inflationary radiation. In this paper, we…
We present a complete analysis of the imprint of tensor anisotropies on the Cosmic Microwave Background for a class of f(R) gravity theories within the PPF-CAMB framework. We derive the equations, both for the cosmological background and gravitational wave perturbations, required to obtain the standard temperature and polarization power spectra, taking care to include all effects which arise from f(R) modifications of both the background and the perturbation equations. For R^n gravity, we show that for n different from 2, the initial conditions in the radiation dominated era are the same as th…
The origin of large scale magnetic fields is one of the most puzzling topics in cosmology and astrophysics. It is assumed that the observed magnetic fields result from the amplification of an initial field produced in the early universe. In this paper we compute the exact power spectrum of magnetic fields created after inflation best known as post inflationary magnetic fields, using the first order cosmological perturbation theory. Our treatment differs from others works because we include an infrared cutoff which encodes only causal modes in the spectrum. The cross-correlation between magneti…
We present cosmological constraints from Planck 2015 data for a universe that is kinetically dominated at very early times. We perform a Markov chain Monte Carlo analysis to estimate parameters and use nested sampling to determine the evidence for a model comparison of the single-field quadratic and Starobinsky inflationary models with the standard $Λ$CDM cosmology. In particular we investigate how different amounts of inflation before and after horizon exit affect the primordial power spectrum and subsequently the power spectrum of the cosmic microwave background. We find that the model using…
In this work we shall consider the effects of a geometrically generated post-inflationary era on the energy spectrum of the primordial gravitational waves. Specifically, we shall consider a post-inflationary constant equation of state era, generated by the synergistic effect of $f(R)$ gravity and of radiation and matter perfect fluids. Two cases of interest shall be studied, one with equation of state parameter $w=-1/3$, in which case the Universe neither accelerates nor decelerates, and one with $w=0$ so an early matter domination era. For the evaluation of the inflationary observational indi…
We investigate constraints on power spectra of the primordial curvature and tensor perturbations with priors based on single-field slow-roll inflation models. We stochastically draw the Hubble slow-roll parameters and generate the primordial power spectra using the inflationary flow equations. Using data from recent observations of CMB and several measurements of geometrical distances in the late Universe, Bayesian parameter estimation and model selection are performed for models that have separate priors on the slow-roll parameters. The same analysis is also performed adopting the standard pa…
A pressing problem in comparing inflationary models with observation is the accurate calculation of correlation functions. One approach is to evolve them using ordinary differential equations ("transport equations"), analogous to the Schwinger-Dyson hierarchy of in-out quantum field theory. We extend this approach to the complete set of momentum space correlation functions. A formal solution can be obtained using raytracing techniques adapted from geometrical optics. We reformulate inflationary perturbation theory in this language, and show that raytracing reproduces the familiar "delta N" Tay…
We consider a model of inflation consisting a single fluid with a time-dependent equation of state. In this phenomenological picture, two periods of inflation are separated by an intermediate non-inflationary stage which can be either a radiation dominated, matter dominated or kinetic energy dominated universe, respectively, with the equation of state $w=1/3$, 0 or 1. We consider the toy model in which the change in $w$ happens instantaneously. Depending on whether the mode of interest leaves the horizon before or after or between the phase transitions, the curvature power spectrum can have no…
The cosmological field equations sourced by a self-interacting scalar field are dynamically equivalent to a closed system of equations obtained by applying the moment method to non-linear Schrödinger equations possessing an underlying non-relativistic conformal $SL(2,\mathbb{R})$ symmetry. We consider the one-dimensional, quintic Schrödinger equation relevant to strongly repulsive, dilute Bose gases. The action of the diffeomorphism group on the space of Schrödinger operators generates an harmonic trapping potential that can be identified with the kinetic energy of the cosmological scalar fiel…
We calculate the quantum gravitational corrections to the Mukhanov-Sasaki equation obtained by the canonical quantization of the inflaton-gravity system. Our approach, which is based on the Born-Oppenheimer decomposition of the resulting Wheeler-DeWitt equation, was previously applied to a minimally coupled inflaton. In this article we examine the case of a non minimally coupled inflaton and, in particular, the induced gravity case is also discussed. Finally, the equation governing the quantum evolution of the inflationary perturbations is derived on a de Sitter background. Moreover the proble…
With the growing consensus on simple power law inflation models not being favored by the PLANCK observations, dynamics for the non-standard inflation gain significant interest in the recent past. In this paper, we analyze in detail a class of supergravity inspired phenomenological inflationary models with non-polynomial potential based on Maity (Nucl.Phys. B919 (2017) 560), and compare the model predictions with the currently most favored Starobinsky and its generalized $α$-attractor models in the ($n_s$ , $r$) plane constrained by PLANCK. Importantly for a wide range of parameter space, our m…
We study static neutron stars in the context of a class of non-minimally coupled inflationary potentials, the universal attractors. Universal attractors are known to generate a viable inflationary era, and they fall into the same category of inflationary phenomenology as the $R^2$ model and other well-known cosmological attractors. We present the essential features of universal attractors in both the Einstein and Jordan frame, and we extract the Tolman-Oppenheimer-Volkoff equations in the Einstein frame using the usual notation of theoretical astrophysics. We use a python 3 based double shooti…
We use a mathematical approach based on the constraints systems in order to reconstruct the equation of state and the inflationary potential for the inflaton field from the observed spectral indices for the density perturbations $n_{s}$ and the tensor to scalar ratio $r$. From the astronomical data, we can observe that the measured values of these two indices lie on a two-dimensional surface. We express these indices in terms of the Hubble slow-roll parameters and we assume that $n_{s}-1=h\left( r\right) $. For the function $h\left( r\right) $, we consider three cases, where $h\left( r\right) …
The simplest inflationary models predict a primordial power spectrum (PPS) of the curvature fluctuations that can be described by a power-law function that is nearly scale-invariant. It has been shown, however, that the low-multipole spectrum of the CMB anisotropies may hint the presence of some features in the shape of the scalar PPS, which could deviate from its canonical power-law form. We study the possible degeneracies of this non-standard PPS with the neutrino anisotropies, the neutrino masses, the effective number of relativistic species and a sterile neutrino or a thermal axion mass. T…
We consider first order perturbation theory for a non-minimally coupled inflaton field without assuming an adiabatic equation of state. In general perturbations in non-minimally coupled theory may be non-adiabatic. However under the slow-roll assumptions the perturbation theory may look like adiabatic one. We show in the frame-work of perturbation theory, that our results of spectral index and bound on no-minimal coupling parameter agree with the results obtained using the adiabatic equation of state by the earlier authors.
There is a widespread belief among inflationary cosmologists that a local observer cannot sense super-horizon gravitons. The argument goes that a local observer would subsume super-horizon gravitons into a redefinition of his coordinate system. We show that adopting this view for pure gravity on de Sitter background leads to time variation in the Hubble parameter measured by a local observer. It also leads to a violation of the gravitational field equation $R = 4 Λ$ because that equation is obeyed by the full metric, rather than the one which has been cleansed of super-horizon modes.
We demonstrate equivalence of the in-in formalism and Green's function method for calculating the bispectrum of primordial gravitational waves generated by vacuum fluctuations of the metric. The tree-level bispectrum from the field equation, $B_h$, agrees with the results obtained previously using the in-in formalism exactly. Characterising non-Gaussianity of the fluctuations using the ratio $B_h/P^2_h$ in the equilateral configuration, where $P_h$ is the power spectrum of scale-invariant gravitational waves, we show that it is much weaker than in models with spectator gauge fields. We also ca…
A new approach is given for the implementation of boundary conditions used in solving the Mukhanov-Sasaki equation in the context of inflation. The familiar quantization procedure is reviewed, along with a discussion of where one might expect deviations from the standard approach to arise. The proposed method introduces a (model dependent) fitting function for the z"/z and a"/a terms in the Mukhanov-Sasaki equation for scalar and tensor modes, as well as imposes the boundary conditions at a finite conformal time. As an example, we employ a fitting function, and compute the spectral index, alon…
With future galaxy surveys, a huge number of Fourier modes of the distribution of the large scale structures in the Universe will become available. These modes are complementary to those of the CMB and can be used to set constraints on models of the early universe, such as inflation. Using a MCMC analysis, we compare the power of the CMB with that of the combination of CMB and galaxy survey data, to constrain the power spectrum of primordial fluctuations generated during inflation. We base our analysis on the Planck satellite and a spectroscopic redshift survey with configuration parameters cl…
We first study dark energy models with a minimally-coupled scalar field and exponential potentials, admitting exact solutions for the cosmological equations: actually, it turns out that for this class of potentials the Einstein field equations exhibit alternative Lagrangians, and are completely integrable and separable (i.e. it is possible to integrate the system analytically, at least by quadratures). We analyze such solutions, especially discussing when they are compatible with a late time quintessential expansion of the universe. As a further issue, we discuss how such quintessential scalar…
We investigate the possibility of constraining the dark energy equation of state by measuring the ratio of Einstein radii in a strong gravitational lens system with two source planes. This quantity is independent of the Hubble parameter and directly measures the growth of angular diameter distances as a function of redshift. We investigate the prospects for a single double source plane system and for a forecast population of systems discovered by re-observing a population of single source lenses already known from a photometrically selected catalogue such as CASSOWARY or from a spectroscopical…
We often find in the literature solutions to the Friedmann and fluid equations for simple cosmological models during the matter, radiation or cosmological constant dominated epochs. However no solutions appear for the inflationary era dominated by the potential energy of a scalar field due, perhaps, to the fact that we do not have as yet a strongly favored model of inflation; there are, of course, very well motivated models which fit the data. The purpose of this article is to study with some detail the evolution of the Universe during inflation in the slow-roll approximation. Taking the Staro…
We derive the power spectrum of primordial quantum fluctuations in an inflationary universe for curvature parameter ${\mathcal K}=1$. This is achieved through a Born--Oppenheimer type of approximation scheme from the Wheeler--DeWitt equation of canonical quantum gravity using gauge-invariant variables. Compared to the flat model, the closed model exhibits a deficit of power at large scales.
We analyse the possible contribution of topological defects to cosmic microwave anisotropies, both temperature and polarisation. We allow for the presence of both inflationary scalars and tensors, and of polarised dust foregrounds that may contribute to or dominate the B-mode polarisation signal. We confirm and quantify our previous statements that topological defects on their own are a poor fit to the B-mode signal. However, adding topological defects to a models with a tensor component or a dust component improves the fit around $\ell=200$. Fitting simultaneously to both temperature and pola…
Random noise arises in many physical problems in which the observer is not tracking the full system. A case in point is inflationary cosmology, the current paradigm for describing the very early universe, where one is often interested only in the time-dependence of a subsystem. In inflationary cosmology it is assumed that a slowly rolling scalar field leads to an exponential increase in the size of space. At the end of this phase, the scalar field begins to oscillate and transfers its energy to regular matter. This transfer typically involves a parametric resonance instability. This article re…
We present a spectroscopic catalog of (mostly) red galaxies in 24 galaxy clusters in the redshift range 0.17 < z < 0.92 obtained with the LRIS instrument on the Keck I telescope. Here we describe the observations and the galaxy spectra, including the discovery of three cD galaxies with LINER emission spectra, and the spectroscopic discovery of four new galaxy-galaxy lenses in cluster environments.
