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Absence of antisymmetric tensor fields : Clue from f(R) model of gravity

Sonej Alam, Somasri Sen, Soumitra Sengupta

Abstract

One of the surprising aspects of the present Universe, is the absence of any noticeable observable effects of higher-rank antisymmetric tensor fields in any natural phenomena. Here, we address the possible explanation of the absence of the higher rank antisymmetric tensor fields within the framework of a general class of $f(R)$ gravity represented by $f (R) = R +α_n R^n$. We explore the setup in Einstein frame, where the higher curvature is manifested in terms of a scalar field with a potential through a conformal transformation. The evolution of different cosmological parameters is studied in the background of FRW universe. We show that while different cosmological parameters mimic their standard behaviour at different epochs for different forms of higher curvature gravity (i.e. different values of n ), the positive values of the scalar field in the models provide an additional suppression for the massless modes of higher rank antisymmetric field, The Starobinsky model identified with $n=2$, provides heavier suppression compared to the others $n\neq2$. The result does not change even with the inclusion of the Cosmological Constant. Thus, our result reveals that a general class of modified gravity models can successfully explain the suppression of the massless modes of higher rank antisymmetric tensor fields leading to their invisibility in the present universe.

Absence of antisymmetric tensor fields : Clue from f(R) model of gravity

Abstract

One of the surprising aspects of the present Universe, is the absence of any noticeable observable effects of higher-rank antisymmetric tensor fields in any natural phenomena. Here, we address the possible explanation of the absence of the higher rank antisymmetric tensor fields within the framework of a general class of gravity represented by . We explore the setup in Einstein frame, where the higher curvature is manifested in terms of a scalar field with a potential through a conformal transformation. The evolution of different cosmological parameters is studied in the background of FRW universe. We show that while different cosmological parameters mimic their standard behaviour at different epochs for different forms of higher curvature gravity (i.e. different values of n ), the positive values of the scalar field in the models provide an additional suppression for the massless modes of higher rank antisymmetric field, The Starobinsky model identified with , provides heavier suppression compared to the others . The result does not change even with the inclusion of the Cosmological Constant. Thus, our result reveals that a general class of modified gravity models can successfully explain the suppression of the massless modes of higher rank antisymmetric tensor fields leading to their invisibility in the present universe.
Paper Structure (11 sections, 27 equations, 6 figures)

This paper contains 11 sections, 27 equations, 6 figures.

Table of Contents

  1. Introduction
  2. $f(R)$ Formalism and Conformal Transformation
  3. Field Equations in Einstein Frame
  4. General class of $f(R)$ : $f(R) = R + \alpha_n R^n$
  5. Different cases of $n$
  6. Case I: $n=2$, Starobinsky model
  7. Case II: $n \neq 2$, $f (R) = R +\alpha_{n} R^n$
  8. $f (R) = R +\alpha_{n} R^n$ models with Cosmological Constant
  9. Results
  10. Discussion and Conclusion
  11. Acknowledgement

Figures (6)

  • Figure 1: Form of potentials for different $n$
  • Figure 2: Evolution of density parameters, scalar field $\tilde{\phi}$ and $\omega_{\tilde{\phi}}$ in Starobinsky model(n=2).
  • Figure 3: Different potentials $V(\tilde{\phi})$, $V_m$ and $V_{eff}$ in Starobinsky model
  • Figure 4: Evolution of different cosmological parameters for $n=-2$ case
  • Figure 5: Different potentials for $n=-2$ case
  • ...and 1 more figures