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Introduction

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Book cover Structure Formation in Modified Gravity Cosmologies

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Abstract

Over the past twenty years or so, a wealth of cosmological observations—ranging from temperature anisotropies in the cosmic microwave background (CMB) (Ade et al., Planck 2015 results. XIII. Cosmological parameters, 2015, [1]), to supernovae type Ia (SNIa) light curves (Riess et al., Astron J 116:1009–1038, 1998, [2], Perlmutter et al., Astrophys J 517:565–586, 1999, [3]), baryonic acoustic oscillations (BAO) imprinted in the galaxy distribution (Cole et al., Mon Not R Astron Soc 362:505–534, 2005, [4], Eisenstein et al., Astrophys J 633:560–574, 2005, [5]) , galaxy cluster abundances (Allen et al., Annu Rev Astron Astrophys 49:409–470, 2007, [6], Ade et al., Planck 2015 results. XXIV. Cosmology from Sunyaev-Zeldovich cluster counts, 2015, [7]), gravitational lensing (Heymans et al., Mon Not R Astron Soc 427:146–166, 2012, [8], Heymans et al., CFHTLenS tomographic weak lensing cosmological parameter constraints: mitigating the impact of intrinsic galaxy alignments, 2013, [9]), etc.—have established the so-called \(\Lambda \) cold dark matter (\(\Lambda \)CDM) model as the standard theoretical paradigm. This model, which assumes the cosmological principle (statistical homogeneity and isotropy on large scales), can be devided into four main ingredients. These are (i) the standard model of particle physics (SMPP); (ii) cold dark matter (CDM); (iii) a cosmological constant, \(\Lambda \); and (iv) general relativity (GR) as the theory of gravity. Next, we briefly discuss each of these in turn (for a more detailed introduction to basic cosmology and the establishment of the \(\Lambda \)CDM model see e.g. the textbooks by Liddle (An introduction to modern cosmology. Wiley, New York, 2003, [10]), Dodelson (Modern cosmology. Academic Press, Amsterdam, 2003, [11]) and Amendola and Tsujikawa (Theory and observations. Cambridge University Press, Cambridge, 2003, [12]).

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Notes

  1. 1.

    This is actually incorrect as electrons are leptons. However, in the literature the word baryons is used to denote electrons as well, which is why we do the same here.

  2. 2.

    Since the coincidence problem is linked to our existence as cosmological observers, there have been attempts to solve this problem using anthropic considerations [28–30]. The argument is that, for instance, life as we know it could only appear after the first galaxies, stars and planets have formed, and therefore we are living soon after the time the Universe became habitable, which would not be that much of a “coincidence”.

  3. 3.

    It is important to stress, however, that modified gravity does not explain the fine tuning problem of \(\Lambda \). Nevertheless, the problem gets relaxed since, if there is now an alternative explanation for dark energy, then the value of \(\Lambda \) can be cancelled exactly, which is easier to motivate (e.g. by some symmetry principle or scenarios of degravitation of \(\Lambda \) [38, 39]) than a case of extreme fine tuning.

  4. 4.

    To the reader less familiar with variational calculus, an action S is an integral over the whole spacetime of the Lagrangian density \(\mathcal {L}\) of a model. The equations of motion for a given physical field that enters the model are obtained from the constrain \(\delta S = 0\), where \(\delta S\) is the variation of S w.r.t. that field. The action is thus a more compact way to describe the physics of a model.

  5. 5.

    In the literature, one often encounters this criterion being described as the amplitude of the matter density fluctuations. This is done perhaps to make the explanations simpler, but is inaccurate. For instance, the matter density perturbation between the Sun and the Earth is small (compared to that of each object), but one still requires the fifth force to be screened there. A more correct description would be made in terms of the gravitational potential (or its gradients), which can be sizeable even if there is a vacuum between two massive bodies.

  6. 6.

    This is precisely what happens in the case of the Galileon model, as we shall see in Chap. 3.

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    Alexandre Barreira

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Barreira, A. (2016). Introduction. In: Structure Formation in Modified Gravity Cosmologies. Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-319-33696-1_1

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