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Register a new userChaotic inflation in modified gravitational theories
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We study chaotic inflation in the context of modified gravitational theories. Our analysis covers models based on (i) a field coupling $omega(phi)$ with the kinetic energy $X$ and a nonmimimal coupling $zeta phi^{2} R/2$ with a Ricci scalar $R$, (ii) Brans-Dicke (BD) theories, (iii) Gauss-Bonnet (GB) gravity, and (iv) gravity with a Galileon correction. Dilatonic coupling with the kinetic energy and/or negative nonminimal coupling are shown to lead to compatibility with observations of the Cosmic Microwave Background (CMB) temperature anisotropies for the self-coupling inflaton potential $V(phi)=lambda phi^{4}/4$. BD theory with a quadratic inflaton potential, which covers Starobinskys $f(R)$ model $f(R)=R+R^{2}/(6M^{2})$ with the BD parameter $omega_{BD}=0$, gives rise to a smaller tensor-to-scalar ratio for decreasing $omega_{BD}$. In the presence of a GB term coupled to the field $phi$, we express the scalar/tensor spectral indices $n_{s}$ and $n_{t}$ as well as the tensor-to-scalar ratio $r$ in terms of two slow-roll parameters and place bounds on the strength of the GB coupling from the joint data analysis of WMAP 7yr combined with other observations. We also study the Galileon-like self-interaction $Phi(phi) X squarephi$ with exponential coupling $Phi(phi) propto e^{muphi}$. Using a CMB likelihood analysis we put bounds on the strength of the Galileon coupling and show that the self coupling potential can in fact be made compatible with observations in the presence of the exponential coupling with $mu>0$.
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Gravitational waves (GW) produced in the early Universe contribute to the number of relativistic degrees of freedom, $N_{rm eff}$, during Big Bang Nucleosynthesis (BBN). By using the constraints on $N_{rm eff}$, we present a new bound on how much the Universe could have expanded between horizon exit of the largest observable scales today and the end of inflation. We discuss the implications on inflationary models and show how the new constraints affect model selection. We also discuss the sensitivities of the current and planned GW observatories such as LIGO and LISA, and show that the constraints they could impose are always less stringent than the BBN bound.
Measuring the primordial power spectrum on small scales is a powerful tool in inflation model building, yet constraints from Cosmic Microwave Background measurements alone are insufficient to place bounds stringent enough to be appreciably effective. For the very small scale spectrum, those which subtend angles of less than 0.3 degrees on the sky, an upper bound can be extracted from the astrophysical constraints on the possible production of primordial black holes in the early universe. A recently discovered observational by-product of an enhanced power spectrum on small scales, induced gravitational waves, have been shown to be within the range of proposed space based gravitational wave detectors; such as NASAs LISA and BBO detectors, and the Japanese DECIGO detector. In this paper we explore the impact such a detection would have on models of inflation known to lead to an enhanced power spectrum on small scales, namely the Hilltop-type and running mass models. We find that the Hilltop-type model can produce observable induced gravitational waves within the range of BBO and DECIGO for integral and fractional powers of the potential within a reasonable number of e-folds. We also find that the running mass model can produce a spectrum within the range of these detectors, but require that inflation terminates after an unreasonably small number of e-folds. Finally, we argue that if the thermal history of the Universe were to accomodate such a small number of e-folds the Running Mass Model can produce Primordial Black Holes within a mass range compatible with Dark Matter, i.e. within a mass range 10^{20}g< M_{BH}<10^{27}g.
We put the upper bound on the gravitational waves (GWs) induced by the scalar-field fluctuations during the inflation. In particular, we focus on the case where the scalar fluctuations get amplified within some subhorizon scales by some mechanism during the inflation. Since the energy conservation law leads to the upper bound on the energy density of the scalar fluctuations, the amplitudes of the scalar fluctuations are constrained and therefore the induced GWs are also. Taking into account this, we derive the upper bound on the induced GWs. As a result, we find that the GW power spectrum must be $mathcal P_h lesssim mathcal O(epsilon^2 (k/k_*)^2)$, where $epsilon$ is the slow-roll parameter and $k_*$ is the peak scale of the scalar-field fluctuations.
Modified gravity theories predict in general a non standard equation for the propagation of gravitational waves. Here we discuss the impact of modified friction and speed of tensor modes on cosmic microwave polarization B modes. We show that the non standard friction term, parametrized by $alpha_{M}$, is degenerate with the tensor-to-scalar ratio $r$, so that small values of $r$ can be compensated by negative constant values of $alpha_M$. We quantify this degeneracy and its dependence on the epoch at which $alpha_{M}$ is different from the standard, zero, value and on the speed of gravitational waves $c_{T}$. In the particular case of scalar-tensor theories, $alpha_{M}$ is constant and strongly constrained by background and scalar perturbations, $0le alpha_{M}< 0.01$ and the degeneracy with $r$ is removed. In more general cases however such tight bounds are weakened and the B modes can provide useful constraints on early-time modified gravity.
In this work, we obtain measurements of the Hubble constant in the context of modified gravity theories. We set up our theoretical framework by considering viable cosmological $f(R)$ and $f(T)$ models, and we analyzed them through the use of geometrical data sets obtained in a model-independent way, namely, gravitationally lensed quasars with measured time delays, standard clocks from cosmic chronometers, and standard candles from the Pantheon Supernovae Ia sample. We find $H_0=(72.4pm 1.4)$ km s$^{-1}$ Mpc$^{-1}$ and $H_0=(71.5pm 1.3)$ km s$^{-1}$ Mpc$^{-1}$ for the $f(R)$ and $f(T)$ models, respectively. Our results represent 1.9% and 1.8% measurements of the Hubble constant, which are fully consistent with the local estimate of $H_0$ by the Hubble Space Telescope. We do not find significant departures from general relativity, as our study shows that the characteristic parameters of the extensions of gravity beyond general relativity are compatible with the $Lambda$CDM cosmology. Moreover, within the standard cosmological framework, our full joint analysis suggests that it is possible to measure the dark energy equation of state parameter at 1.2% accuracy, although we find no statistical evidence for deviations from the cosmological constant case.
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