Tensor perturbations in inflationary models as a probe of cosmology

Effects of a Geometrically Realized Early Dark Energy Era on the Spectrum of Primordial Gravitational Waves

In this work, we investigate the effects of a geometrically generated early dark energy era on the energy spectrum of the primordial gravitational waves. The early dark energy era, which we choose to have a constant equation of state parameter w, is synergistically generated by an appropriate f(R) gravity in the presence of matter and radiation perfect fluids. As we demonstrate, the predicted signal for the energy spectrum of the f(R) primordial gravitational waves is amplified and can be detectable, for various reheating temperatures, especially for large reheating temperatures. The signal amplitude depends on the duration of the early dark energy era and on the value of the dark energy equation of state parameter, with the latter affecting more crucially the amplification. Specifically, the amplification occurs when the equation of state parameter approaches the de Sitter value w=−1. Regarding the duration of the early dark energy era, we find that the largest amplification occurs when the early dark energy era commences at temperature T=0.85 eV until T=7.8 eV. Moreover, we study a similar scenario in which amplification occurs, where the early dark energy era commences at T=0.29 eV and lasts until the temperature is increased by ΔT∼1.7 eV. The discovery of primordial gravitational waves will reveal if several symmetries in the Universe exist or not so this work is important toward revealing the primordial gravitational waves.

Spectrum of Primordial Gravitational Waves in Modified Gravities: A Short Overview

In this work, we shall exhaustively study the effects of modified gravity on the energy spectrum of the primordial gravitational waves background. S. Weinberg has also produced significant works related to the primordial gravitational waves, with the most important one being the effects of neutrinos on primordial gravitational waves. With this short review, our main aim is to gather all the necessary information for studying the effects of modified gravity on primordial gravitational waves in a concrete and quantitative way and in a single paper. After reviewing all the necessary techniques for extracting the general relativistic energy spectrum, and how to obtain, in a WKB way, the modified gravity damping or amplifying factor, we concentrate on specific forms of modified gravity of interest. The most important parameter involved for the calculation of the effects of modified gravity on the energy spectrum is the parameter aM, which we calculate for the cases of f(R,ϕ) gravity, Chern–Simons-corrected f(R,ϕ) gravity, Einstein–Gauss–Bonnet-corrected f(R,ϕ) gravity, and higher derivative extended Einstein–Gauss–Bonnet-corrected f(R,ϕ) gravity. The exact form of aM is presented explicitly for the first time in the literature. With regard to Einstein–Gauss–Bonnet-corrected f(R,ϕ) gravity, and higher derivative extended Einstein–Gauss–Bonnet-corrected f(R,ϕ) gravity theories, we focus on the case in which the gravitational wave propagating speed is equal to that of light in a vacuum. We provide expressions for aM expressed in terms of the cosmic time and in terms of the redshift, which can be used directly for the numerical calculation of the effect of modified gravity on the primordial gravitational wave energy spectrum.

Implications of the NANOGrav results for inflation

The NANOGrav pulsar timing array experiment reported evidence for a stochastic common-spectrum process affecting pulsar timing residuals in its 12.5-yr data set, which might be interpreted as the first detection of a stochastic gravitational wave background (SGWB). I examine whether the NANOGrav signal might be explained by an inflationary SGWB, focusing on the implications for the tensor spectral index nT and the tensor-to-scalar ratio r. Explaining NANOGrav while complying with upper limits on r from BICEP2/Keck Array and Planck requires $r \gtrsim {\cal O}(10^{-6})$ in conjunction with an extremely blue tensor spectrum, 0.7 ≲ nT ≲ 1.3. After discussing models, which can realize such a blue spectrum, I show that this region of parameter space can be brought in agreement with big bang nucleosynthesis constraints for a sufficiently low reheating scale, $T_{\rm rh} \lesssim 100\, {\rm GeV} \!-\! 1\, {\rm TeV}$. With the important caveat of having assumed a power-law parametrization for the primordial tensor spectrum, an inflationary interpretation of the NANOGrav signal is therefore not excluded.

Detection methods for stochastic gravitational-wave backgrounds: a unified treatment

We review detection methods that are currently in use or have been proposed to search for a stochastic background of gravitational radiation. We consider both Bayesian and frequentist searches using ground-based and space-based laser interferometers, spacecraft Doppler tracking, and pulsar timing arrays; and we allow for anisotropy, non-Gaussianity, and non-standard polarization states. Our focus is on relevant data analysis issues, and not on the particular astrophysical or early Universe sources that might give rise to such backgrounds. We provide a unified treatment of these searches at the level of detector response functions, detection sensitivity curves, and, more generally, at the level of the likelihood function, since the choice of signal and noise models and prior probability distributions are actually what define the search. Pedagogical examples are given whenever possible to compare and contrast different approaches. We have tried to make the article as self-contained and comprehensive as possible, targeting graduate students and new researchers looking to enter this field.

Inflationary predictions for scalar and tensor fluctuations reconsidered

We reconsider the predictions of inflation for the spectral index of scalar (energy density) fluctuations (ns) and the tensor/scalar ratio (r) using a discrete, model-independent measure of the degree of fine-tuning required to obtain a given combination of (ns, r ). We find that, except for cases with numerous unnecessary degrees of fine-tuning, ns is less than 0.98, measurably different from exact Harrison-Zel'dovich. Furthermore, if ns >or= 0.95, in accord with current measurements, the tensor/scalar ratio satisfies r >or= 10(-2), a range that should be detectable in proposed cosmic microwave background polarization experiments and direct gravitational wave searches.