Simplest Inflationary Models Research Articles

Parity-violating trispectrum from Chern-Simons gravity

A potential source for parity violation in the Universe is inflation. The simplest inflationary models have two fields: the inflaton and graviton, and the lowest-order parity-violating coupling between them is dynamical Chern-Simons (dCS) gravity with a decay constant f. Here, we show that dCS imprints a parity-violating signal in primordial scalar perturbations. Specifically, we find that, after dCS amplifies one graviton helicity due to a tachyonic instability, the graviton-mediated correlation between two pairs of scalars develops a parity-odd component. This correlation, the primordial scalar trispectrum, is then transferred to the corresponding curvature correlator and thus is imprinted in both large-scale structure (LSS) and the cosmic microwave background (CMB). We find that the parity-odd piece has roughly the same amplitude as its parity-even counterpart, scaled linearly by the degree of gravitational circular polarization Πcirc ∼ √ε[h 2/(M Pl f)] ≤ 1, with ε the slow-roll parameter, H the inflationary Hubble scale, and the upper bound saturated for purely circularly-polarized gravitons. We also find that, in the collapsed limit, the ratio of the two trispectra contains direct information about the graviton's spin. In models beyond standard inflationary dCS, e.g. those with multiple scalar fields or superluminal scalar sound speed, there can be a large enhancement factor F ≳ 106 to the trispectrum. We find that an LSS survey that contains N modes linear modes would place an nσ constraint on Πcirc r of ∼ 0.04 (n/3)(106/F)(106/N modes)1/2 from the parity-odd galaxy trispectrum, for tensor-to-scalar ratio r. We also forecast for several spectroscopic and 21-cm surveys. This constraint implies that, for high-scale single-field inflation parameters, LSS can probe very large dCS decay constants f ≲ 4 × 109 GeV(3/n)(F/106)(N modes/106)1/2. Our result is the first example of a massless particle yielding a parity-odd scalar trispectrum through spin-exchange.

Inflation in Pakistan

This paper examines the factors that explain and help forecast inflation in Pakistan. A simple inflation model is specified that includes standard monetary variables (money supply, credit to the private sector), an activity variable, the interest and the exchange rates, as well as the wheat support price as a supply-side factor. The model is estimated for the period January 1998 to June 2005 on a monthly basis. The results indicate that monetary factors have played a dominant role in recent inflation, affecting inflation with a lag of about one year. Private sector credit growth and broad money growth are also good leading indicators of inflation which can be used to forecast future inflation developments. JEL classification: E31, C22, C32 Keywords: Inflation, Pakistan, Leading Indicators, Forecasting, Monetary Policy

What moves the heavens above?

The standard cosmological model (ΛCDM) assumes that everything started in a singular Big Bang out of Cosmic Inflation, a mysterious form of modern Aether (the inflaton). Here we look for direct observational evidence for such beginning in two recent measurements: 1) cosmic acceleration, something ΛCDM attributes to Dark Energy (DE), 2) discordant measurements for H0 and anomalies in the CMB. We find here that observed variations in H0 correspond to large metric perturbations that are not consistent with the simplest models of Inflation or DE in the ΛCDM paradigm. Together, these observations indicate instead that cosmic expansion could originate from a simple gravitational collapse and bounce. We conjecture that such bounce is trigger by neutron degeneracy at GeV energies. This new paradigm explains the heavens above using only the known laws of Physics, without any new Aether, DE or Inflation.

Hidden dark matter from Starobinsky inflation

The Starobinsky inflation model is one of the simplest inflation models that is consistent with the cosmic microwave background observations. In order to explain dark matter of the universe, we consider a minimal extension of the Starobinsky inflation model with introducing the dark sector which communicates with the visible sector only via the gravitational interaction. In Starobinsky inflation model, a sizable amount of dark-sector particle may be produced by the inflaton decay. Thus, a scalar, a fermion or a vector boson in the dark sector may become dark matter. We pay particular attention to the case with dark non-Abelian gauge interaction to make a dark glueball a dark matter candidate. In the minimal setup, we show that it is difficult to explain the observed dark matter abundance without conflicting observational constraints on the coldness and the self-interaction of dark matter. We propose scenarios in which the dark glueball, as well as other dark-sector particles, from the inflaton decay become viable dark matter candidates. We also discuss possibilities to test such scenarios.

The imprint of primordial gravitational waves on the CMB intensity profile

We use the induced geometry on the two dimensional transverse cross section of a photon beam propagating on a perturbed Friedmann-Robertson-Walker (FRW) spacetime to find the Cosmic Microwave Background (CMB) photon distribution over a telescope's collecting area today. It turns out that at each line of sight the photons are diluted along a transverse direction due to gravitational shearing. The effect can be characterized by two spin-weight-two variables, which are reminiscent of the Stokes polarization parameters. Similar to that case, one can construct a scalar and a pseudo-scalar function where the latter only gets contributions from the tensor modes. We analytically determine the power spectrum of the pseudo-scalar at superhorizon scales in a simple inflationary model and briefly discuss possible observational consequences.

Primordial black holes from inflaton fragmentation into oscillons

We show that fragmentation of the inflaton into long-lived spatially localized oscillon configurations can lead to copious production of black holes. In simple inflation models primordial black holes of sublunar mass can form, and they can account for all of the dark matter. We also explore the possibility that solar-mass primordial black holes, particularly relevant for gravitational wave astronomy, are produced from the same mechanism.

Dark neutrino interactions make gravitational waves blue

New interactions of neutrinos can stop them from free-streaming in the early Universe even after the weak decoupling epoch. This results in the enhancement of the primordial gravitational wave amplitude on small scales compared to the standard $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ prediction. In this paper, we calculate the effect of dark matter neutrino interactions in CMB tensor $B$-modes spectrum. We show that the effect of new neutrino interactions generates a scale- or $\ensuremath{\ell}$-dependent imprint in the CMB $B$-modes power spectrum at $\ensuremath{\ell}\ensuremath{\gtrsim}100$. In the event that primordial $B$-modes are detected by future experiments, a departure from scale invariance, with a blue spectrum, may not necessarily mean failure of simple inflationary models but instead may be a sign of nonstandard interactions of relativistic particles. New interactions of neutrinos also induce a phase shift in the CMB $B$-mode power spectrum which cannot be mimicked by simple modifications of the primordial tensor power spectrum. There is rich information hidden in the CMB $B$-modes spectrum beyond just the tensor-to-scalar ratio.

Pure natural inflation

We point out that a simple inflationary model in which the axionic inflaton couples to a pure Yang–Mills theory may give the scalar spectral index (ns) and tensor-to-scalar ratio (r) in complete agreement with the current observational data.

Inflationary primordial black holes for the LIGO gravitational wave events and pulsar timing array experiments

Primordial black holes (PBHs) are one of the candidates to explain the gravitational wave (GW) signals observed by the LIGO detectors. Among several phenomena in the early Universe, cosmic inflation is a major example to generate PBHs from large primordial density perturbations. In this paper, we discuss the possibility to interpret the observed GW events as mergers of PBHs which are produced by cosmic inflation. The primordial curvature perturbation should be large enough to produce a sizable amount of PBHs and thus we have several other probes to test this scenario. We point out that the current pulsar timing array (PTA) experiments already put severe constraints on GWs generated via the second-order effects, and that the observation of the cosmic microwave background (CMB) puts severe restriction on its $\mu$ distortion. In particular, it is found that the scalar power spectrum should have a very sharp peak at $k \sim 10^{6}$ Mpc$^{-1}$ to fulfill the required abundance of PBHs while evading constraints from the PTA experiments together with the $\mu$ distortion. We propose a mechanism which can realize such a sharp peak. In the future, simple inflation models that generate PBHs via almost Gaussian fluctuations could be probed/excluded.

Reheating constraints in quintessential inflation

We study the consequences of reheating in quintessential inflation. From simple inflationary quintessential models introduced in cite{hap, hap2}, we show that when the reheating is due to the production of heavy massive particles conformally coupled with gravity, a viable model which matches with the current observational data cite{Ade, Planck, bicep2} is only possible for reheating temperatures that range between $1$ GeV and $10^4$ GeV. On the other hand, when the universe reheats via the production of massless particles, the viability of the model is only possible when those particles are nearly conformally coupled with gravity, leading to a reheating temperature between $1$ MeV and $10^4$ GeV.

Inflationary magnetogensis in R2-inflation on the light of Planck 2015

We study the primordial magnetic field (PMF) generated by the simple inflationary model f2FF in the context of R2-inflationary model, the favourite model of Planck 2015 results. The scale invariant PMF is achieved and the backreaction problem is avoided as long as, the rate of inflationary expansion, H, is less than the upper bound reported by Planck, 2015, in the observable scales of wave numbers, kη. Based on these results, we find that the upper limit of present magnetic field, B0 < 8.1 × 10−9G . It is in the same order of the one reported by Planck, 2015.

CMBB-mode non-Gaussianity

We study the degree to which the cosmic microwave background (CMB) can be used to constrain primordial non-Gaussianity involving one tensor and two scalar fluctuations, focusing on the correlation of one polarization $B$ mode with two temperature modes. In the simplest models of inflation, the tensor-scalar-scalar primordial bispectrum is non-vanishing and is of the same order in slow-roll parameters as the scalar-scalar-scalar bispectrum. We calculate the $\langle BTT\rangle$ correlation arising from a primordial tensor-scalar-scalar bispectrum, and show that constraints from an experiment like CMB-Stage IV using this observable are more than an order of magnitude better than those on the same primordial coupling obtained from temperature measurements alone. We argue that $B$-mode non-Gaussianity opens up an as-yet-unexplored window into the early Universe, demonstrating that significant information on primordial physics remains to be harvested from CMB anisotropies.

Simple brane-world inflationary models — An update

In the light of the Planck 2015 results, we update simple inflationary models based on the quadratic, quartic, Higgs and Coleman–Weinberg potentials in the context of the Randall–Sundrum brane-world cosmology. Brane-world cosmological effect alters the inflationary predictions of the spectral index [Formula: see text] and the tensor-to-scalar ratio [Formula: see text] from those obtained in the standard cosmology. In particular, the tensor-to-scalar ratio is enhanced in the presence of the 5th dimension. In order to maintain the consistency with the Planck 2015 results for the inflationary predictions in the standard cosmology, we find a lower bound on the five-dimensional Planck mass [Formula: see text]. On the other hand, the inflationary predictions laying outside of the Planck allowed region can be pushed into the allowed region by the brane-world cosmological effect with a suitable choice of [Formula: see text].

Simple inflationary models in Gauss–Bonnet brane-world cosmology

In light of the recent Planck 2015 results for the measurement of the cosmic microwave background (CMB) anisotropy, we study simple inflationary models in the context of the Gauss–Bonnet (GB) brane-world cosmology. The brane-world cosmological effect modifies the power spectra of scalar and tensor perturbations generated by inflation and causes a dramatic change for the inflationary predictions of the spectral index (ns) and the tensor-to-scalar ratio (r) from those obtained in the standard cosmology. In particular, the predicted r values in the inflationary models favored by the Planck 2015 results are suppressed due to the GB brane-world cosmological effect, which is in sharp contrast with inflationary scenario in the Randall–Sundrum brane-world cosmology, where the r values are enhanced. Hence, these two brane-world cosmological scenarios are distinguishable. With the dramatic change of the inflationary predictions, the inflationary scenario in the GB brane-world cosmology can be tested by more precise measurements of ns and future observations of the CMB B-mode polarization.

Simple inflationary quintessential model

In the framework of a flat Friedmann-Lema{\^\i}tre-Robertson-Walker (FLRW) geometry, we present a nonsingular model (no big bang singularity at finite time) of our universe describing its evolution starting from its early inflationary era up to the present accelerating phase. We found that a hydrodynamical fluid with nonlinear equation of state could result in such a non singular scenario, which after the end of this inflationary stage, suffers a sudden phase transition and enters into the stiff matter dominated era, and the universe becomes reheated due to a huge amount of particle production. Finally, it asymptotically enters into the de Sitter phase concluding the present accelerated expansion. We show that the background providing an inflationary potential leads to a power spectrum of the cosmological perturbations which fit well with the latest Planck estimations. At the end, we compared our viable potential with some known inflationary quintessential potentials, which shows that, our model is an improved version of them because it contains an analytic solution that allows us to perform analytic calculations.

Open EFTs, IR effects &amp; late-time resummations: systematic corrections in stochastic inflation

Though simple inflationary models describe the CMB well, their corrections are often plagued by infrared effects that obstruct a reliable calculation of late-time behaviour. We adapt to cosmology tools designed to address similar issues in other physical systems with the goal of making reliable late-time inflationary predictions. The main such tool is Open EFTs which reduce in the inflationary case to Stochastic Inflation plus calculable corrections. We apply this to a simple inflationary model that is complicated enough to have dangerous IR behaviour yet simple enough to allow the inference of late-time behaviour. We find corrections to standard Stochastic Inflationary predictions for the noise and drift, and we find these corrections ensure the IR finiteness of both these quantities. The late-time probability distribution, ${\cal P}(\phi)$, for super-Hubble field fluctuations are obtained as functions of the noise and drift and so these too are IR finite. We compare our results to other methods (such as large-$N$ models) and find they agree when these models are reliable. In all cases we can explore in detail we find IR secular effects describe the slow accumulation of small perturbations to give a big effect: a significant distortion of the late-time probability distribution for the field. But the energy density associated with this is only of order $H^4$ at late times and so does {\em not} generate a dramatic gravitational back-reaction.

String gas cosmology after Planck

We review the status of string gas cosmology (SGC) after the 2015 Planck data release. SGC predicts an almost scale-invariant spectrum of cosmological perturbations with a slight red tilt, like the simplest inflationary models. It also predicts a scale-invariant spectrum of gravitational waves with a slight blue tilt, unlike inflationary models which predict a red tilt of the gravitational wave spectrum. SGC yields two consistency relations which determine the tensor to scalar ratio and the slope of the gravitational wave spectrum given the amplitude and tilt of the scalar spectrum. We show that these consistency relations are in good agreement with the Planck data. We discuss future observations which will be able to differentiate between the predictions of inflation and those of SGC.

Quantum corrections to inflaton dynamics: The semiclassical approach and the semiclassical limit

Computations of quantum corrections to the CMB spectrum and to scalar field dynamics during inflation very often take advantage of the "semi-classical" approach, where the metric fluctuations are simply omitted. On the other hand, a complete computation ought to take into account that the matter field perturbation and scalar metric perturbation together constitute a single physical degree of freedom. The question then naturally arises, in which sense the semi-classical approach is an approximation to the complete calculation, and whether there are specific limits where this is also a good approximation. We consider the quantum corrected dynamics of interacting scalar fields in an expanding inflationary background. We demonstrate this by explicitly computing the leading quantum radiative corrections to the evolution equation of the mean field ("condensate") and the Friedmann equations taking into account scalar perturbations of both the matter field and the metric, and when omitting the latter. We find that the two agree in the limit H << M_pl , but one is not a limit of the other. We also find that in simple models of inflation, H/M_pl is not small enough that the two approaches can be said to agree. By direct comparison, we demonstrate how to interpret the "semi-classical" approach often employed in more complex computations as a well-defined approximation, and quantify its validity.

Inflationary perturbations in bimetric gravity

In this paper we study the generation of primordial perturbations in a cosmological setting of bigravity during inflation. We consider a model of bigravity which can reproduce the ΛCDM background and large scale structure and a simple model of inflation with a single scalar field and a quadratic potential. Reheating is implemented with a toy-model in which the energy density of the inflaton is entirely dissipated into radiation. We present analytic and numerical results for the evolution of primordial perturbations in this cosmological setting. We find that the amplitude of tensor perturbations generated during inflation is sufficiently suppressed to avoid the effects of the tensor instability discovered in refs. [1,2] which develops during the cosmological evolution in the physical sector. We argue that from a pure analysis of the tensor perturbations this bigravity model is compatible with present observations. However, we derive rather stringent limits on inflation from the vector and scalar sectors.

PROSPECTS FOR DELENSING THE COSMIC MICROWAVE BACKGROUND FOR STUDYING INFLATION

A detection of excess cosmic microwave background (CMB) B-mode polarization on large scales allows the possibility of measuring not only the amplitude of these fluctuations but also their scale dependence, which can be parametrized as the tensor tilt nT. Measurements of this scale dependence will be hindered by the secondary B-mode polarization anisotropy induced by gravitational lensing. Fortunately, these contaminating B modes can be estimated and removed with a sufficiently good estimate of the intervening gravitational potential and a good map of CMB E-mode polarization. We present forecasts for how well these gravitational lensing B modes can be removed, assuming that the lensing potential can be estimated either internally from CMB data or using maps of the cosmic infrared background (CIB) as a tracer. We find that CIB maps are as effective as CMB maps for delensing at the noise levels of the current generation of CMB experiments, while the CMB maps themselves will ultimately be best for delensing at polarization noise below = 1 μK arcmin. At this sensitivity level, CMB delensing will be able to measure nT to an accuracy of 0.02 or better, which corresponds to the tensor tilt predicted by the consistency relation for single-field slow-roll models of inflation with r = 0.2. However, CIB-based delensing will not be sufficient for constraining nT in simple inflationary models.