Abstract:We propose a simple toy model for quintessential inflation where a complex scalar field described by a lagrangian with a U (1) P Q symmetry spontaneously broken at a high energy scale and explicitly broken by instanton effects at a much lower energy can account for both the early inflationary phase and the recent accelerated expansion of the Universe. The real part of the complex field plays the role of the inflaton whereas the imaginary part, the "axion", is the quintessence field.
“…Similar to natural inflation [107], it has been proposed that the flatness of the quintessnce potential could be protected by the field being a pseudo-Nambu-Goldstone boson [108,109]. Additionally, it has been proposed that dark energy and inflation can both be driven by the same field [110][111][112][113][114][115][116][117][118] Quintessence models have a rich phenomenology; one of the more interesting phenomena is that-by suitably choosing the potential-the energy density in the quintessence field can be made to "track" the energy density in radiation/matter at early times and then grow to dominate the energy budget at late times [119][120][121][122][123][124][125][126]. The canonical example of a potential that produces this behavior is the Ratra-Peebles potential [67] V (φ) = M 4+n φ n , (2.4) where n > 0 is a constant.…”
After a decade and a half of research motivated by the accelerating universe, theory and experiment have a reached a certain level of maturity. The development of theoretical models beyond Λ or smooth dark energy, often called modified gravity, has led to broader insights into a path forward, and a host of observational and experimental tests have been developed. In this review we present the current state of the field and describe a framework for anticipating developments in the next decade. We identify the guiding principles for rigorous and consistent modifications of the standard model, and discuss the prospects for empirical tests.We begin by reviewing recent attempts to consistently modify Einstein gravity in the infrared, focusing on the notion that additional degrees of freedom introduced by the modification must "screen" themselves from local tests of gravity. We categorize screening mechanisms into three broad classes: mechanisms which become active in regions of high Newtonian potential, those in which first derivatives of the field become important, and those for which second derivatives of the field are important. Examples of the first class, such as f (R) gravity, employ the familiar chameleon or symmetron mechanisms, whereas examples of the last class are galileon and massive gravity theories, employing the Vainshtein mechanism. In each case, we describe the theories as effective theories and discuss prospects for completion in a more fundamental theory. We describe experimental tests of each class of theories, summarizing laboratory and solar system tests and describing in some detail astrophysical and cosmological tests. Finally, we discuss prospects for future tests which will be sensitive to different signatures of new physics in the gravitational sector.The review is structured so that those parts that are more relevant to theorists vs. observers/experimentalists are clearly indicated, in the hope that this will serve as a useful reference for both audiences, as well as helping those interested in bridging the gap between them.
“…Similar to natural inflation [107], it has been proposed that the flatness of the quintessnce potential could be protected by the field being a pseudo-Nambu-Goldstone boson [108,109]. Additionally, it has been proposed that dark energy and inflation can both be driven by the same field [110][111][112][113][114][115][116][117][118] Quintessence models have a rich phenomenology; one of the more interesting phenomena is that-by suitably choosing the potential-the energy density in the quintessence field can be made to "track" the energy density in radiation/matter at early times and then grow to dominate the energy budget at late times [119][120][121][122][123][124][125][126]. The canonical example of a potential that produces this behavior is the Ratra-Peebles potential [67] V (φ) = M 4+n φ n , (2.4) where n > 0 is a constant.…”
After a decade and a half of research motivated by the accelerating universe, theory and experiment have a reached a certain level of maturity. The development of theoretical models beyond Λ or smooth dark energy, often called modified gravity, has led to broader insights into a path forward, and a host of observational and experimental tests have been developed. In this review we present the current state of the field and describe a framework for anticipating developments in the next decade. We identify the guiding principles for rigorous and consistent modifications of the standard model, and discuss the prospects for empirical tests.We begin by reviewing recent attempts to consistently modify Einstein gravity in the infrared, focusing on the notion that additional degrees of freedom introduced by the modification must "screen" themselves from local tests of gravity. We categorize screening mechanisms into three broad classes: mechanisms which become active in regions of high Newtonian potential, those in which first derivatives of the field become important, and those for which second derivatives of the field are important. Examples of the first class, such as f (R) gravity, employ the familiar chameleon or symmetron mechanisms, whereas examples of the last class are galileon and massive gravity theories, employing the Vainshtein mechanism. In each case, we describe the theories as effective theories and discuss prospects for completion in a more fundamental theory. We describe experimental tests of each class of theories, summarizing laboratory and solar system tests and describing in some detail astrophysical and cosmological tests. Finally, we discuss prospects for future tests which will be sensitive to different signatures of new physics in the gravitational sector.The review is structured so that those parts that are more relevant to theorists vs. observers/experimentalists are clearly indicated, in the hope that this will serve as a useful reference for both audiences, as well as helping those interested in bridging the gap between them.
“…In this paper, we have studied the constraints on a simple model of quintessential inflation previously proposed by us [7] that arise from the WMAP3 CMB and SDSS LRG data. We find that the effective scale of symmetry breaking, f, must be larger than about 3 M Pl in order to satisfy the constraints on the scalar spectral index and the tensor-toscalar ratio from inflation at the 68% CL.…”
Section: Discussionmentioning
confidence: 99%
“…In Ref. [7], we introduced a simple, wellmotivated model that unifies these two fields into a single complex scalar field. We briefly review this model below.…”
We derive constraints on a simple quintessential inflation model, based on a spontaneously broken 4 theory, imposed by the Wilkinson Microwave Anisotropy Probe three-year data (WMAP3) and by galaxy clustering results from the Sloan Digital Sky Survey (SDSS). We find that the scale of symmetry breaking must be larger than about 3 Planck masses in order for inflation to generate acceptable values of the scalar spectral index and of the tensor-to-scalar ratio. We also show that the resulting quintessence equation of state can evolve rapidly at recent times and hence can potentially be distinguished from a simple cosmological constant in this parameter regime.
“…When having N fields, our relations should of course be modified. In the simple case that the parameters of the N fields are identical, to convert the formulae in the text to the new case, we should make the following changes: To summarize, our purpose has been to give a step forward starting from the idea of Frieman and Rosenfeld [8] that fields in a potential may supply a unified explanation of inflation and dark energy. Our model contains two scalar fields, one complex and one real, and a potential that contains a non-symmetric part due to Planck-scale physics.…”
We present a model with a complex and a real scalar fields and a potential whose symmetry is explicitly broken by Planck-scale physics. For exponentially small breaking, the model accounts for the period of inflation in the early universe and for the period of acceleration of the late universe.
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