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Cosmological relevance of scaling solutions: A recipe for quintessential inflation

Abstract

In this brief review, we describe (asymptotic) scaling behaviour that manifests in the scalar field dynamics in the presence of background energy density (radiation/matter). We highlight the role of scaling solutions in model building for dark energy and quintessential inflation.

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There is no data available for this manuscript.

Notes

  1. Scalar field has a variable equation of state parameter which interpolates between \(+1\) and \(-1\). A slowly rolling scalar field can easily comply with the observation according to which latte times acceleration is caused by an exotic fluid with equation of state that lies close \(-1\) (including \(-1\)). It can trivially mimic cosmological constant. Thus slowly rolling scalar field in cosmology is just next to the cosmological constant. Secondly, late time acceleration might be the left over effect from inflation − quintessential inflation. After inflation ends, scalar field (inflaton) might evolve in a generic fashion hiding itself through the entire thermal history, emerge only at late times rolling slowly. Last but not least, late time dynamics is independent of initial conditions, if scalar field exhibits scaling behaviour \(\omega _\phi =\omega _b=const\).

  2. Given a shallow potential, scalar field rolls down its potential slowly and might give rise to successful inflation. Inflationary dynamics is solely determined by the field potential; no matter fields are believed to be present, they are created during preheating after inflation. On the other hand, due to the presence of background matter in the post inflationary era, scalar field (with runaway steep potential) can show a distinguished behaviour qualitatively different from the inflationary era.

  3. We imagine that field commences evolution on the steep part of the potential.

  4. In this case, reheating takes place due to alternative mechanism responsible for matter creation [57].

  5. Relation (11) is implied by evolution equations in case of scaling solution and should not be confused with slow roll which is clear from right hand side of (11). Infect, in this case, one is dealing with steep potential and fast roll. Thus (11) is specific to scaling solution. This equation readily integrates to yield the characteristic behaviour of scaling regime given by (12).

  6. Field dominated solution is accelerating if \(\lambda ^2<2\); potential is sufficiently shallow or nearly flat in this case.

  7. It should be noted that slow roll can occur in the presence of background matter even if field potential is steep. This precisely happens when \(\rho _\phi<<\rho _b\) and evolution of universe is determined by the background matter. The latter induces a huge Hubble damping forcing the field to freeze along its steep potential. This phenomenon, reminds Hubble damping in brane world cosmology due to high energy brane corrections. Scalar field dynamics in general and slow roll, in particular, in presence of background matter is quite different from inflationary dynamics, see Ref. [4] for details.

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Acknowledgements

We thank Shibesh kumar, Mohit K Sharma and Nur Jaman for useful discussions. RM was supported by the Ministry of Education and Science of Kazakhstan, Grant AP09261147.

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Correspondence to M. Sami.

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Dedicated to the memories of T. Padmanabhan, to be included in the Padmanabhan memorial special issue of GERG.

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Sami, M., Myrzakulov, R. Cosmological relevance of scaling solutions: A recipe for quintessential inflation. Gen Relativ Gravit 54, 86 (2022). https://doi.org/10.1007/s10714-022-02969-6

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Keywords

  • Scaling solution
  • Asymptotic scaling
  • Quintessential inflation
  • Preheating
  • Exit mechanism