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Register a new userFrame-dependence of inflationary observables in scalar-tensor gravity
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Alexandros Karam Dr.
Publication date
2019
fields
Physics
and research's language is
English
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By means of the Greens function method, we computed the spectral indices up to third order in the slow-roll approximation for a general scalar-tensor theory in both the Einstein and Jordan frames. Using quantities which are invariant under the conformal rescaling of the metric and transform as scalar functions under the reparametrization of the scalar field, we showed that the frames are equivalent up to this order due to the underlying assumptions. Nevertheless, care must be taken when defining the number of $e$-folds.
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In this paper we investigate the asymptotic dynamics of inflationary cosmological models that are based in scalar-tensor theories of gravity. Our main aim is to explore the global structure of the phase space in the framework of single-field inflation models. For this purpose we make emphasis in the adequate choice of the variables of the phase space. Our results indicate that, although single-field inflation is generic in the sense that the corresponding critical point in the phase space exists for a wide class of potentials, along given phase space orbits -- representing potential cosmic histories -- the occurrence of the inflationary stage is rather dependent on the initial conditions. We have been able to give quantitative estimates of the relative probability (RP) for initial conditions leading to slow-roll inflation. For the non-minimal coupling model with the $phi^2$-potential our rough estimates yield to an almost vanishing relative probability: $10^{-13},%lesssim RPll 10^{-8},%$. These bonds are greatly improved in the scalar-tensor models, including the Brans-Dicke theory, where the relative probability $1,%lesssim RPleq 100,%$. Hence slow-roll inflation is indeed a natural stage of the cosmic expansion in Brans-Dicke models of inflation. It is confirmed as well that the dynamics of vacuum Brans-Dicke theories with arbitrary potentials are non-chaotic.
In this work we shall study the implications of a subclass of $E$-models cosmological attractors, namely of $a$-attractors, on hydrodynamically stable slowly rotating neutron stars. Specifically, we shall present the Jordan frame theory of the $a$-attractors, and by using a conformal transformation we shall derive the Einstein frame theory. We discuss the inflationary context of $a$-attractors in order to specify the allowed range of values for the free parameters of the model based on the latest cosmic-microwave-background-based Planck 2018 data. Accordingly, using the notation and physical units frequently used in theoretical astrophysics contexts, we shall derive the Tolman-Oppenheimer-Volkoff equations in the Einstein frame. Assuming a piecewise polytropic equation of state, the lowest density part of which shall be chosen to be the WFF1, or APR or the SLy EoS, we numerically solve the Tolman-Oppenheimer-Volkoff equations using a double shooting python-based LSODA numerical code. The resulting picture depends on the value of the parameter $a$ characterizing the $a$-attractors. As we show, for large values of $a$, which do not produce a viable inflationary era, the $M-R$ graphs are nearly identical to the general relativistic result, and these two are discriminated at large central densities values. Also, for large $a$-values, the WFF1 equation of state is excluded, due to the GW170817 constraints. In addition, the small $a$ cases produce larger masses and radii compared to the general relativistic case and are compatible with the GW170817 constraints on the radii of neutron stars. Our results indicate deep and not yet completely understood connections between non-minimal inflationary attractors and neutron stars phenomenology in scalar-tensor theory.
In this paper the scalar-tensor theory of gravity is assumed to describe the evolution of the universe and the gravitational scalar $phi$ is ascribed to play the role of inflaton. The theory is characterized by the specified coupling function $omega(phi)$ and the cosmological function $lambda(phi)$. The function $lambda(phi)$ is nearly constant for $0<phi<0.1$ and $lambda(1)=0$. The functions $lambda(phi)$ and $omega(phi)$ provide a double-well potential for the motion of $phi(t)$. Inflation commences and ends naturally by the dynamics of the scalar field. The energy density of matter increases steadily during inflation. When the constant $Gamma$ in the action is determined by the present matter density, the temperature at the end of inflation is of the order of $10^{14} GeV$ in no need of reheating. Furthermore, the gravitational scalar is just the cold dark matter that men seek for.
With a scalar field non-minimally coupled to curvature, the underlying geometry and variational principle of gravity - metric or Palatini - becomes important and makes a difference, as the field dynamics and observational predictions generally depend on this choice. In the present paper we describe a classification principle which encompasses both metric and Palatini models of inflation, employing the fact that inflationary observables can be neatly expressed in terms of certain quantities which remain invariant under conformal transformations and scalar field redefinitions. This allows us to elucidate the specific conditions when a model yields equivalent phenomenology in the metric and Palatini formalisms, and also to outline a method how to systematically construct different models in both formulations that produce the same observables.
We study the screening mechanism in the most general scalar-tensor theories that leave gravitational waves unaffected and are thus compatible with recent LIGO/Virgo observations. Using the effective field theory of dark energy approach, we consider the general action for perturbations beyond linear order, focussing on the quasi-static limit. When restricting to the subclass of theories that satisfy the gravitational wave constraints, the fully nonlinear effective Lagrangian contains only three independent parameters. One of these, $beta_1$, is uniquely present in degenerate higher-order theories. We compute the two gravitational potentials for a spherically symmetric matter source and we find that for $beta_1 ge 0$ they decrease as the inverse of the distance, as in standard gravity, while the case $beta_1 < 0$ is ruled out. For $beta_1 > 0$, the two potentials differ and their gravitational constants are not the same on the inside and outside of the body. Generically, the bound on anomalous light bending in the Solar System constrains $beta_1 lesssim 10^{-5}$. Standard gravity can be recovered outside the body by tuning the parameters of the model, in which case $beta_1 lesssim 10^{-2}$ from the Hulse-Taylor pulsar.
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