Gravity Rainbow Effects on Higher Curvature Modification of R2 inflation

Abstract

In this work, we study several extensions of the higher curvature modification of $R^2$ inflation in the context of gravity's rainbow. We modify the $(R+R^2)$ model by adding an $f_1{R}^3$-term, an $f_2{R}^4$-term, and an $f_3{R}^{3/2}$-term to the original model. We calculate the inflationary observables and confront them using the latest observational bounds from Planck 2018 data. We assume the rainbow function of the form $\tilde{f}=1+{\left(\frac{H}{M}\right)}^{\lambda }$ with $\lambda$ being a rainbow parameter and $M$ a mass-dimensional parameter. We demonstrate that the power spectrum of curvature perturbation relies on the dimensionless coefficient $f_i,i=1,2,3$, a rainbow parameter $\lambda$ and a ratio $H/M$. Likewise, the scalar spectral index $n_s$ is affected by both $f_i$ and the rainbow parameter. Moreover, the tensor-to-scalar ratio $r$ is solely determined by the rainbow parameter. Interestingly, by ensuring that $n_s$ aligns with the Planck collaboration's findings at the $1\sigma$ confidence level, the tensor-to-scalar ratio could reach up to $r\sim 0.01$, which is possibly measurable for detection in forthcoming Stage IV CMB ground experiments and is certainly feasible for future dedicated space missions.

arXiv commentv3: 21 pages, 4 figures. references added, texts modified, results unchanged. Version published in EPJC. arXiv admin note: text overlap with arXiv:2404.14766

References in corpus (49)

• f(R) Theories Of Gravity
• Unified cosmic history in modified gravity: from F(R) theory to Lorentz non-invariant models
• f(R) theories
• Modified Gravity Theories on a Nutshell: Inflation, Bounce and Late-time Evolution
• Gravity's Rainbow
• Inflationary cosmology in modified gravity theories
• Recent Advances on Inflation
• On the Starobinsky Model of Inflation from Supergravity
• Nearly Starobinsky inflation from modified gravity
• A polynomial f(R) inflation model
• Remnant for all Black Objects due to Gravity's Rainbow
• Charged Dilatonic Black Holes in Gravity's Rainbow
• Absence of Black Holes at LHC due to Gravity's Rainbow
• Thermodynamic phase transition of a black hole in rainbow gravity
• Absence of an Effective Horizon for Black Holes in Gravity's Rainbow
• Effects of energy dependent spacetime on geometrical thermodynamics and heat engine of black holes: gravity's rainbow
• Charged BTZ black holes in the context of massive gravity's rainbow
• Black Holes in Gauss-Bonnet Gravity's Rainbow
• Critical behavior of charged black holes in Gauss-Bonnet gravity`s rainbow
• Remnants of Black Rings from Gravity's Rainbow
• Nonsingular Universes in Gauss-Bonnet Gravity's Rainbow
• Higher Order Corrections in Minimal Supergravity Models of Inflation
• Inflationary universe from higher-derivative quantum gravity
• Trace-anomaly driven inflation in modified gravity and the BICEP2 result
• Consistency relation for $R^p$ inflation
• Analytic extensions of Starobinsky model of inflation
• Bouncing inflation in nonlinear $R^2+R^4$ gravitational model
• On the covariant formalism of the effective field theory of gravity and leading order corrections
• Recovering MOND from extended metric theories of gravity
• Reconstructing the inflationary $f(R)$ from observations
• Inflation and dark energy from f(R) gravity
• Old-minimal supergravity models of inflation
• F(R) gravity's rainbow and its Einstein counterpart
• Gravitational Collapse in Gravity's Rainbow
• Black hole thermodynamics in Lovelock gravity's rainbow with (A)dS asymptote
• Starobinsky Model in Rainbow Gravity
• Reheating after f(R) inflation
• Spotting deviations from R^2 inflation
• Beyond-one-loop quantum gravity action yielding both inflation and late-time acceleration
• Deformed Starobinsky model in gravity's rainbow
• $R^2\log R$ quantum corrections and the inflationary observables
• Marginally Deformed Starobinsky Gravity
• Vaidya Spacetime in Massive Gravity's Rainbow
• Disentangling the $f(R)$ - Duality
• $R^n$ Extension of Starobinsky Model in Old Minimal Supergravity
• $Ad{S}_4$ dyonic black holes in gravity's rainbow
• Inflation from $f(R)$ theories in gravity's rainbow
• Towards a formulation of $f(R)$ supergravity
• ${\mathcal{R}}^2$ Quantum Corrected Scalar Field Inflation

Cited by in corpus (2)

• Inflation in Myrzakulov $F(R,T)$ Gravity: A Comparative Study in Metric, Symmetric Teleparallel, and Weitzenböck Formalisms
• Gravitational baryogenesis in $F(R)$ gravity's rainbow