Using the Reduced Relativistic Gas (RRG) model, we analytically determine the matter power spectrum for Warm Dark Matter (WDM) on small scales, $k>1 htext{/Mpc}$. The RRG is a simplified model for the ideal relativistic gas, but very accurate in the
cosmological context. In another work, we have shown that, for typical allowed masses for dark matter particles, $m>5 text{keV}$, the higher order multipoles, $ell>2$, in the Einstein-Boltzmann system of equations are negligible on scales $k<10 htext{/Mpc}$. Hence, we can follow the perturbations of WDM using the ideal fluid framework, with equation of state and sound speed of perturbations given by the RRG model. We derive a Meszaros like equation for WDM and solve it analytically in radiation, matter and dark energy dominated eras. Joining these solutions, we get an expression that determines the value of WDM perturbations as a function of redshift and wavenumber. Then we construct the matter power spectrum and transfer function of WDM on small scales and compare it to some results coming from Lyman-$alpha$ forest observations. Besides being a clear and pedagogical analytical development to understand the evolution of WDM perturbations, our power spectrum results are consistent with the observations considered and the other determinations of the degree of warmness of dark matter particles.
We perform a comprehensive study of gravitational waves in the context of the higher-order quadratic-scalar-curvature gravity, which encompasses the ordinary Einstein-Hilbert term in the action plus a $R^{2}$-contribution and a term of the type $Rsqu
are R$. The main focus is on gravitational waves emitted by binary systems such as binary black holes and binary pulsars in the approximation of circular orbits and non-relativistic motion. The waveform of higher-order gravitational waves from binary black holes is constructed and compared with the waveform predicted by standard general relativity; we conclude that the merger occurs before in our model than what would be expected from GR. The decreasing rate of the orbital period in binary pulsars is used to constraint the coupling parameters of our higher-order $R^{2}$-gravity; this is done with Hulse-Taylor binary pulsar data leading to $kappa_{0}^{-1}lesssim1.1times10^{16},text{m}^{2}$, where $kappa_{0}^{-1}$ is the coupling constant for the $R^{2}$-contribution.
The Reduced Relativistic Gas (RRG) is a simplified version of the ideal relativistic gas, which assumes that all particles have the same momentum magnitude. Although this is a very idealized situation, the resulting model preserves the phenomenology
of Maxwell-Boltzmann distribution and, in some situations, can be described as a perfect fluid, without introducing large errors in both cosmological background and first-order perturbations. The perfect fluid description of RRG model was already used to study the warmness of dark matter, massive neutrinos and interaction of baryons and photons before recombination, showing very good agreement with previous works based on the full Einstein-Boltzmann system of equations. In order to understand these results and construct a more general and formal framework for RRG, we develop a theoretical description of first-order cosmological perturbations of RRG, based on a distribution function which encodes the simplifying assumption that all particles have the same momentum magnitude. The full set of Einstein-Boltzmann equations for RRG distribution are derived and quantities beyond the perfect fluid approximation are studied. Using RRG to describe warm dark matter, we show that, for particles with $m sim text{keV}$, the perfect fluid approximation is valid on scales $k < 10, text{h}/text{Mpc}$, for most of the universe evolution. We also determine initial conditions for RRG in the early universe and study the evolution of potential in a toy model of universe composed only by RRG.
An extension of the Starobinsky model is proposed. Besides the usual Starobinsky Lagrangian, a term proportional to the derivative of the scalar curvature, $ abla_{mu}R abla^{mu}R$, is considered. The analyzis is done in the Einstein frame with the i
ntroduction of a scalar field and a vector field. We show that inflation is attainable in our model, allowing for a graceful exit. We also build the cosmological perturbations and obtain the leading-order curvature power spectrum, scalar and tensor tilts and tensor-to-scalar ratio. The tensor and curvature power spectrums are compared to the most recent observations from BICEP2/Keck collaboration. We verify that the scalar-to-tensor rate $r$ can be expected to be up to three times the values predicted by Starobinsky model.
In Cuzinatto et al. [Phys. Rev. D 93, 124034 (2016)], it has been demonstrated that theories of gravity in which the Lagrangian includes terms depending on the scalar curvature $R$ and its derivatives up to order $n$, i.e. $fleft(R, abla_{mu}R, abla_
{mu_{1}} abla_{mu_{2}}R,dots, abla_{mu_{1}}dots abla_{mu_{n}}Rright)$ theories of gravity, are equivalent to scalar-multitensorial theories in the Jordan frame. In particular, in the metric and Palatini formalisms, this scalar-multitensorial equivalent scenario shows a structure that resembles that of the Brans-Dicke theories with a kinetic term for the scalar field with $omega_{0}=0$ or $omega_{0}=-3/2$, respectively. In the present work, the aforementioned analysis is extended to the Einstein frame. The conformal transformation of the metric characterizing the transformation from Jordans to Einsteins frame is responsible for decoupling the scalar field from the scalar curvature and also for introducing a usual kinetic term for the scalar field in the metric formalism. In the Palatini approach, this kinetic term is absent in the action. Concerning the other tensorial auxiliary fields, they appear in the theory through a generalized potential. As an example, the analysis of an extension of the Starobinsky model (with an extra term proportional to $ abla_{mu}R abla^{mu}R$) is performed and the fluid representation for the energy-momentum tensor is considered. In the metric formalism, the presence of the extra term causes the fluid to be an imperfect fluid with a heat flux contribution; on the other hand, in the Palatini formalism the effective energy-momentum tensor for the extended Starobinsky gravity is that of a perfect fluid type. Finally, it is also shown that the extra term in the Palatini formalism represents a dynamical field which is able to generate an inflationary regime without a graceful exit.
In this work, the hydrogens ionization energy was used to constrain the free parameter $b$ of three Born-Infeld-like electrodynamics namely Born-Infeld itself, Logarithmic electrodynamics and Exponential electrodynamics. An analytical methodology cap
able of calculating the hydrogen ground state energy level correction for a generic nonlinear electrodynamics was developed. Using the experimental uncertainty in the ground state energy of the hydrogen atom, the bound $b>5.37times10^{20}Kfrac{V}{m}$, where $K=2$, $4sqrt{2}/3$ and $sqrt{pi}$ for the Born-Infeld, Logarithmic and Exponential electrodynamics respectively, was established. In the particular case of Born-Infeld electrodynamics, the constraint found for $b$ was compared with other constraints present in the literature.
Bopp-Podolsky electrodynamics is generalized to curved space-times. The equations of motion are written for the case of static spherically symmetric black holes and their exterior solutions are analyzed using Bekensteins method. It is shown the solut
ions split-up into two parts, namely a non-homogeneous (asymptotically massless) regime and a homogeneous (asymptotically massive) sector which is null outside the event horizon. In addition, in the simplest approach to Bopp-Podolsky black holes, the non-homogeneous solutions are found to be Maxwells solutions leading to a Reissner-Nordstrom black hole. It is also demonstrated that the only exterior solution consistent with the weak and null energy conditions is the Maxwells one. Thus, in light of energy conditions, it is concluded that only Maxwell modes propagate outside the horizon and, therefore, the no-hair theorem is satisfied in the case of Bopp-Podolsky fields in spherically symmetric space-times.
The equivalence between theories depending on the derivatives of $R$, i.e. $fleft( R, abla R,..., abla^{n}Rright) $, and scalar-multi-tensorial theories is verified. The analysis is done in both metric and Palatini formalisms. It is shown that $fleft
( R, abla R,..., abla^{n}Rright) $ theories are equivalent to scalar-multi-tensorial ones resembling Brans-Dicke theories with kinetic terms $omega_{0}=0$ and $omega_{0}= - frac{3}{2}$ for metric and Palatini formalisms respectively. This result is analogous to what happens for $f(R)$ theories. It is worthy emphasizing that the scalar-multi-tensorial theories obtained here differ from Brans-Dicke ones due to the presence of multiple tensorial fields absent in the last. Furthermore, sufficient conditions are established for $fleft( R, abla R,..., abla^{n}Rright) $ theories to be written as scalar-multi-tensorial theories. Finally, some examples are studied and the comparison of $fleft( R, abla R,..., abla^{n}Rright) $ theories to $fleft( R,Box R,...Box^{n}Rright) $ theories is performed.
We propose a phenomenological unified model for dark matter and dark energy based on an equation of state parameter $w$ that scales with the $arctan$ of the redshift. The free parameters of the model are three constants: $Omega_{b0}$, $alpha$ and $be
ta$. Parameter $alpha$ dictates the transition rate between the matter dominated era and the accelerated expansion period. The ratio $beta / alpha$ gives the redshift of the equivalence between both regimes. Cosmological parameters are fixed by observational data from Primordial Nucleosynthesis (PN), Supernovae of the type Ia (SNIa), Gamma-Ray Bursts (GRB) and Baryon Acoustic Oscillations (BAO). The calibration of the 138 GRBs events is performed using the 580 SNIa of the Union2.1 data set and a new set of 79 high-redshift GRBs is obtained. The various sets of data are used in different combinations to constraint the parameters through statistical analysis. The unified model is compared to the $Lambda$CDM model and their differences are emphasized.
We investigate the causal structure of general nonlinear electrodynamics and determine which Lagrangians generate an effective metric conformal to Minkowski. We also proof that there is only one analytic nonlinear electrodynamics presenting no birefringence.
