R2 Gravity Research Articles

Cosmological collider non-Gaussianity from multiple scalars and R2 gravity

Cosmological collider signals of primordial non-Gaussianity arise at tree level when an extra scalar has Hubble mass during inflation. We critically review the formalism finding that a large class of inflationary theories, based on Planck-scale physics, predict a scalar bi-spectrum around the gravitational floor level. This mild signal arises for example in R2 gravity, in the regime where its gravitational scalar has Hubble-scale mass. Signals much above the gravitational floor arise in theories where scalars undergo multiple turns during inflation, thanks to sub-Planckian physics.

Non-triviality of an asymptotically flat vacuum spacetime in pure R2 gravity

In [Phys. Rev. D 107, 104008 (2023)], we reported a novel exact closed-form solution which describes asymptotically flat spacetimes in pure [Formula: see text] gravity. The solution is Ricci scalar flat, viz. [Formula: see text] everywhere. Whereas any metric with a null Ricci scalar would trivially satisfy the [Formula: see text] vacuo field equation, [Formula: see text], in this paper, we shall show that our solution satisfies a “stronger” version of the [Formula: see text] vacuo field equation, viz. [Formula: see text], despite the term [Formula: see text] being singular. Even though [Formula: see text] identically vanishes, for our solution, the combinations [Formula: see text] and [Formula: see text] are free of singularity. This exceptional property sets our solution apart from the set of null-Ricci-scalar metrics and makes it a genuinely nontrivial solution. We further demonstrate that, as a member of a larger class of asymptotically de Sitter metrics, our solution is resilient against perturbations in the scalar curvature at largest distances, making it relevant for physical situations where the background deviates from asymptotic flatness.

Observational test of ℛ2 spacetimes with the S2 star in the Milky Way galactic center

A novel class of vacuum metrics expressible in analytical form was recently found for pure ℛ2 gravity, based on a groundwork put forth by Buchdahl in 1962. These Buchdahl-inspired solutions offer a practical framework for testing ℛ2 gravity through empirical observations. Within a subclass of asymptotically flat Buchdahl-inspired vacuum spacetimes, we identified a parameter ϵ measuring the deviation from the classic Schwarzschild metric, which corresponds to ϵ=0. In this paper, we employ observational data from the S2 star's orbit around Sgr A* in the Milky Way galactic center and perform Monte Carlo Markov Chain simulations to probe the effects of the new metrics on the orbit of the S2 star. Our analysis presented herein reports a range at 95% confidence level on the deviation parameter as ϵ ∈ (-0.6690, 0.4452). While no decisive evidence either in favor or in disfavor of the asymptotically flat Buchdahl-inspired spacetimes has been achieved, the obtained bound is compatible with the tighter results using other data of different nature as recently reported in Eur. Phys. J. C 84 (2024) 330. As a meaningful test probing into a strong-field regime, our present study calls for further observations with prolonged period and improved accuracy in order to tighten the bound for ϵ using the S2 star orbit.

Wormhole inducing exponential expansion in R2 gravity

Wormholes are considered both from the Wheeler deWitt equation, as well as from the field equations in the Euclidean background of Robertson Walker mini-superspace in [Formula: see text] gravity. Quantum wormhole satisfies Hawking Page wormhole boundary condition in the Euclidean background of mini-superspace, however, in the Lorentzian background wave functional turns to the usual oscillatory function. The Euclidean field equations for [Formula: see text] lead to the wormhole configuration, as well as oscillating universe in Euclidean time [Formula: see text]. The oscillating universe in Euclidean time [Formula: see text] transforms to an expanding universe only for [Formula: see text] in Lorentz time [Formula: see text] under analytic continuation [Formula: see text] and asymptotically leads to an exponential solution. An Euclidean wormhole in the very early era evolves to an oscillating universe in [Formula: see text], thereafter crossing deSitter radius transition to an inflationary era is evident at later epoch only for [Formula: see text].

On the degrees of freedom of R2 gravity in flat spacetime

We study the degrees of freedom of R2 gravity in flat spacetime with two approaches. By rewriting the theory a la Stueckelberg, and implementing Lorentz-like gauges to the metric perturbations, we confirm that the pure theory propagates one scalar degree of freedom, while the full theory contains two tensor modes in addition. We then consider the degrees of freedom by directly examining the metric perturbations. We show that the degrees of freedom of the full theory match with those obtained with the manifestly covariant approach. In contrast, we find that the pure R2 gravity has no degrees of freedom. We show that a similar discrepancy between the two approaches appears also in a theory dual to the three-form, and appears due to the Lorentz-like gauges, which lead to the fictitious modes even after the residual gauge redundancy has been taken into account. At first sight, this implies a discontinuity between the full theory and the pure case. By studying the first-order corrections of the full R2 gravity beyond the linear regime, we show that at high-energies, both scalar and tensor degrees of freedom become strongly coupled. This implies that the apparent discontinuity of pure and full R2 gravity is just an artefact of the perturbation theory, and further supports the absence of degrees of freedom in the pure R2 gravity.

Closed Timelike Curves Induced by a Buchdahl-Inspired Vacuum Spacetime in R2 Gravity

The recently obtained special Buchdahl-inspired metric Phys. Rev. D 107, 104008 (2023) describes asymptotically flat spacetimes in pure Ricci-squared gravity. The metric depends on a new (Buchdahl) parameter k˜ of higher-derivative characteristic, and reduces to the Schwarzschild metric, for k˜=0. For the case k˜∈(−1,0), it was shown that it describes a traversable Morris–Thorne–Buchdahl (MTB) wormhole Eur. Phys. J. C 83, 626 (2023), where the weak energy condition is formally violated. In this paper, we briefly review the special Buchdahl-inspired metric, with focuses on the construction of the Kruskal–Szekeres (KS) diagram and the situation for a wormhole to emerge. Interestingly, the MTB wormhole structure appears to permit the formation of closed timelike curves (CTCs). More specifically, a CTC straddles the throat, comprising of two segments positioned in opposite quadrants of the KS diagram. The closed timelike loop thus passes through the wormhole throat twice, causing two reversals in the time direction experienced by the (timelike) traveller on the CTC. The key to constructing a CTC lies in identifying any given pair of antipodal points (T,X) and (−T,−X) on the wormhole throat in the KS diagram as corresponding to the same spacetime event. It is interesting to note that the Campanelli–Lousto metric in Brans–Dicke gravity is known to support two-way traversable wormholes, and the formation of the CTCs presented herein is equally applicable to the Campanelli–Lousto solution.

Bardeen Tolman–Kuchowicz spheres in logarithmic-corrected R2 gravity

This study enlightens the effect of electric charge in the context of Logarithmic-corrected [Formula: see text] gravity model by assuming the specific form of metric potentials [Formula: see text] and [Formula: see text], known as Tolman–Kuchowicz spacetime. The key feature of our study is to assume the Bardeen model to narrate the nature of exterior geometry. This discussion enhances the analysis as the Bardeen black hole solution can be formulated as a gravitationally collapsed magnetic monopole which arises from some particular case of nonlinear electrodynamics. Further, the modified matching conditions, designed for [Formula: see text] gravity, have been imposed to compute all the unknown constants involved in metric potentials for the qualitative evaluation of the study. For this purpose, we have studied all the mandatory characteristics of stellar structures like energy density, pressure components, energy bonds, equilibrium condition, stability constraints, mass–radius relation. A comprehensive graphical analysis to ensure the credibility of the [Formula: see text] gravity model has been presented. It is worth indicating that our obtained charged anisotropic outcomes are physically well-fitted with the best degree of accuracy.

Warm deformed R2 inflation

In this work, we study warm inflationary scenario based on a deformation of R2 gravity. We start considering Rp and assume p=2(1+δ) with δ≪1 so that we simply obtain warm R2 inflation when setting δ=0. We then derive the potential in the Einstein frame and consider a dissipation parameter of the form Γ=C1T with C1 being a coupling parameter. We focus only on the strong regime of which the interaction between inflaton and radiation fluid has been taken into account. We also consider a detailed analysis of the background dynamics, considering the evolution of the relevant quantities. We compute inflationary observables and constrain the parameters of our model using latest observational data reported by Planck. From our analysis, we discover that with proper choices of parameters the derived ns and r are in good agreement with the Planck 2018 observational constraints. Particularly, we constrain the potential scale U0 of the models.

R2 gravity effects on the kinetic axion phase space

In this work we consider the effect of an R 2 term on the kinetic misalignment axion theory. By using the slow-roll assumptions during inflation and the field equations, we construct an autonomous dynamical system for the kinetic axion, including the effects of the R 2 term and we solve numerically the dynamical system. As we demonstrate, the pure kinetic axion attractor is transposed to the right in the field phase space, and it is no longer , but it is , with some non-zero value of the scalar field with . This feature indicates that the kinetic axion mechanism is enhanced, and the axion oscillations are further delayed, compared with the pure kinetic axion case. The phenomenological implications on the duration of the inflationary era, on the commencing of the reheating era and the reheating temperature, are also discussed.

Disc partition function of 2d R2 gravity from DWG matrix model

We compute the sum over flat surfaces of disc topology with arbitrary number of conical singularities. To that end, we explore and generalize a specific case of the matrix model of dually weighted graphs (DWG) proposed and solved by one of the authors, M. Staudacher and Th. Wynter. Namely, we compute the sum over quadrangulations of the disc with certain boundary conditions, with parameters controlling the number of squares (area), the length of the boundary and the coordination numbers of vertices. The vertices introduce conical defects with angle deficit given by a multiple of π, corresponding to positive, zero or negative curvature. Our results interpolate between the well-known 2d quantum gravity solution for the disc with fluctuating 2d metric and the regime of “almost flat” surfaces with all the negative curvature concentrated on the boundary. We also speculate on possible ways to study the fluctuating 2d geometry with AdS2 background instead of the flat one.

Pre-inflationary bounce effects on primordial gravitational waves of f(R) gravity

In this work we shall study a possible pre-inflationary scenario for our Universe and how this might be realized by f(R) gravity. Specifically, we shall introduce a scenario in which the Universe in the pre-inflationary era contracts until it reaches a minimum magnitude, and subsequently expands, slowly entering a slow-roll quasi-de Sitter inflationary era. This pre-inflationary bounce avoids the cosmic singularity, and for the eras before and after the quasi-de Sitter inflationary stage, approximately satisfies the string theory motivated scale factor duality a(t)=a−1(−t). We investigate which approximate forms of f(R) can realize such a non-singular pre-inflationary scenario, the quasi-de Sitter patch of which is described by an R2 gravity, thus the exit from inflation is guaranteed. Furthermore, since in string theory pre-Big Bang scenarios lead to an overall amplification of the gravitational wave energy spectrum, we examine in detail this perspective for the f(R) gravity generating this pre-inflationary non-singular bounce. As we show, in the f(R) gravity case, the energy spectrum of the primordial gravitational waves background is also amplified, however the drawback is that the amplification is too small to be detected by future high frequency interferometers. Thus we conclude that, as in the case of single scalar field theories, f(R) gravity cannot produce detectable stochastic gravitational waves and a synergistic theory of scalars and higher order curvature terms might be needed.

Exact models of pure radiation in R2 gravity for spatially homogeneous wave-like Shapovalov spacetimes type II

Presented are exactly integrable models with pure radiation in R2 gravity with a cosmological constant related to wave-like Shapovalov spacetimes type II. Spatially homogeneous models of Shapovalov spacetimes were considered. The obtained solutions belong to spaces of type III according to the Bianchi classification and of type N according to the Petrov classification. For the models under consideration, exact solutions for the equations of motion of test particles are obtained in the Hamilton–Jacobi formalism. For the obtained exact models, solutions of the geodesic deviation equations are obtained.

Collapsing stellar structures in [formula omitted] gravity using Karmarkar condition

Our study illuminates the effects of gravitational collapse by considering heat flux anisotropic matter sources within the framework of the f(R) theory of gravity. We assume the non-static spherically symmetric configuration to narrate the nature of the interior spacetime and match it with the Vaidya exterior geometry. Further, we employ the well-known Karmarkar condition, as it reduces the solution-generating method of field equations to a single metric potential. To ensure the viability of our collapsing system, a comprehensive graphical analysis is presented in the context of the Logarithmic-corrected R2 gravity model. Our investigation argues that there are no traces of trapped surfaces in the collapsing procedure. Thus, naked singularity and black hole are not the final fate of the gravitational collapse.

Pure R2 gravity can gravitate about a flat background

Pure R2 gravity (R2 gravity by itself with no Einstein-Hilbert term) has attracted attention because it is different from other quadratic gravity theories. In a curved de Sitter (dS) or anti-de Sitter (AdS) background, it is equivalent to Einstein gravity with an additional massless scalar and with a cosmological constant. In contrast to other higher-derivative theories, it is therefore unitary. The equivalence with Einstein gravity is not valid for a flat background. In fact, it has been shown that linearizations of pure R2 gravity about flat spacetime does not produce a graviton. In other words, it does not gravitate about flat space. Pure R2 gravity is invariant under restricted Weyl transformations where the metric is scaled by a conformal factor that obeys a harmonic condition. In this work we consider an action composed of pure R2 gravity, a massless scalar field φ non-minimally coupled to gravity plus other terms. The entire action is invariant under restricted Weyl transformations. We show that when the scalar field φ acquires a non-zero vacuum expectation value (VEV), flat spacetime now becomes a viable gravitating background solution. The restricted Weyl symmetry becomes broken, not explicitly but spontaneously. In other words, when φ acquires a non-zero VEV, the equivalent Einstein action has now the possibility of having a zero cosmological constant and therefore solutions in a Minkowski background. The action can also have, as before, a non-zero cosmological constant, so that solutions in a dS and AdS background are still possible.

Cosmological models in R2 gravity with hybrid expansion law

In this paper, evolution of a Friedmann–Robertson–Walker universe is studied in a higher derivative theory of gravity. The relativistic solutions admitting hybrid expansion law of the universe are explored here. Hybrid expansion law is a general form of scale factor from which one can recover both the power-law expansion and exponential expansion as a special case. The hybrid expansion law is interesting as it addresses the early deceleration phase and presents accelerating phase satisfactorily. It is found that an inflationary scenario with hybrid expansion law is permitted in the [Formula: see text] gravity fairly well. We consider universe filled with cosmic fluid that describes by an equation of state (EoS) parameter which varies with time. Consequently, we analyze the time variation of energy density parameter, cosmic pressure, equation of state parameter, deceleration parameter and jerk parameter in the cosmological model. The constraints of the model parameters imposed by the cosmological observational data set are determined. The present value of the deceleration parameter [Formula: see text], EoS parameter and the epoch at which the transition of decelerated phase to accelerated phase are estimated. In the higher derivative theory, we obtain some new and interesting cosmological solutions relevant for building cosmological models.

Strongest constraint in f(R) = R+ α R2 gravity: stellar stability

In the metric approach of f(R) theories of gravity, the fourth-order field equations are often recast as effective Einstein equations in the presence of standard matter and a curvature fluid (which gathers all the extra terms), always in the Jordan frame. In this picture, we investigate the strong gravity regime of the f(R) = R+ α R2 model. In particular, we focus on the stability of a compact star composed by a mixture of ordinary matter—described by a polytropic equation of state—and an effective curvature fluid in an otherwise standard Einstein gravity, so that we are able to apply the usual equations that govern the radial adiabatic oscillations of relativistic stars. Our new restriction on the free parameter is α ≲ 2.4 × 108 cm2 in order to guarantee stellar stability, about 010 times more restrictive than previous results (based on mass-radius relations alone) in the literature.

On the linear stability of polytropic fluid spheres in R2 gravity

Within [Formula: see text] gravity, we study the linear stability of strongly gravitating spherically symmetric configurations supported by a polytropic fluid. All calculations are carried out in the Jordan frame. It is demonstrated that, as in general relativity, the transition from stable to unstable systems occurs at the maximum of the curve mass-central density of the fluid.

Rotating neutron stars in F(R) gravity with axions

ABSTRACT We investigate equilibrium configurations of uniformly rotating neutron stars in R2 gravity with axion scalar field for GM1 equation of state (EoS) for nuclear matter. The mass–radius diagram, mass–central energy density are presented for some frequencies in comparison with static stars. We also compute equatorial and polar radii and moment of inertia for stars. For axion field ϕ, the coupling in the form ∼R2ϕ is assumed. Several interesting results follow from our consideration. Maximal possible star mass with given EoS increases due to the contribution of coupling term. We discovered the possibility to increase maximal frequency of the rotation in comparison with General Relativity. As a consequence, the lower bound on mass of the fast rotating stars decreases. For frequency f = 700 Hz, neutron stars with masses ∼M⊙ can exist for some choice of parameters (in General Relativity for same EoS, this limit is around 1.2 M⊙). Another feature of our solutions is relatively small increase of stars' radii for high frequencies in comparison with static case. Thus, eventually, the new class of neutron stars in R2 gravity with axions is discovered namely fast rotating compact stars with intermediate masses.

Weyl scaling invariant R2 gravity for inflation and dark matter

Inflation in the early universe can generate the nearly conformal invariant fluctuation that leads to the structures we observe at the present. The simple viable Starobinsky R2 inflation has an approximate global scale symmetry. We study the conformal symmetric Weyl Rˆ2 and general F(Rˆ) theories and demonstrate their equivalence to Einstein gravity coupled with a scalar and a Weyl gauge field. The scalar field in Weyl Rˆ2 gravity can be responsible for inflation with Starobinsky model as the attractor, potentially distinguishable from the latter by future experiments. The intrinsic Weyl gauge boson becomes massive once the Einstein frame is fixed, and constitutes as a dark matter candidate with mass up to ∼5×1016GeV.

Power-law Inflation with Scalar Field assisted R2 Gravity: a perturbative approach

It is shown that power-law inflation (PLI) in general relativity (GR)-based cosmology can be realized due to the f(R) gravity corrections to the standard GR action. In this paper, we have considered ϵR2 correction to the GR-based PLI model, and then apply the perturbation theory to first order to explore the effects of ϵR2 correction on the results obtained from GR-based PLI model. This model has the ability to resolve the problems arise in GR-based PLI model. We calculate scalar spectral index, tensor-to-scalar ratio, running of spectral index, which are in very good agreement with recent Planck2018 data. An interesting feature of this model is that it has a graceful exit to radiation-dominated stage which is induced by the ϵR2 correction.