The Standard Cosmological Model

The Standard Model of Particle Physics (SMPP) is an enormously successful description of high energy physics, driving ever more precise measurements to find ‘physics beyond the standard model’, as well as providing motivation for developing more fundamental ideas that might explain the values of its parameters. Simultaneously, a description of the entire 3-dimensional structure of the present-day Universe is being built up painstakingly. Most of the structure is stochastic in nature, being merely the result of the particular realisation of the ‘initial conditions’ within our observable Universe patch. However, governing this structure is the Standard Model of Cosmology (SMC), which appears to require only about a dozen parameters. Cosmologists are now determining the values of these quantities with increasing precision in order to search for ‘physics beyond the standard model’, as well as trying to develop an understanding of the more fundamental ideas which might explain the values of its parameters. Although it is natural to see analogies between the two Standard Models, some intrinsic differences also exist, which are discussed here. Nevertheless, a truly fundamental theory will have to explain both the SMPP and SMC, and this must include an appreciation of which elements are deterministic and which are accidental. Considering different levels of stochasticity within cosmology may make it easier to accept that physical parameters in general might have a non-deterministic aspect. PACS Nos.: 98.80.-k, 98.80.Bp, 98.80.Es, 12.60.-i 1. The Two Standard Models Probably the most audacious endeavours in modern physical science are: (1) the attempt to understand the laws governing the whole of physical reality down to the smallest imaginable scales; and (2) the attempt to find a quantitative description of the properties of the entire Universe on the largest scales. Since the Universe is known to be expanding and cooling, then these two quests become linked at the earliest epochs, and hence fundamental physics and cosmology are necessarily connected. We do not yet have a complete theory to describe high energy physics, but at below TeV energies our understanding is on extremely firm ground. The combination of Quantum Chromodynamics with Electroweak Theory is known as the Standard Model of Particle Physics (hereafter SMPP). The SMPP was solidified in the early 1970s and has been incredibly well tested since then (see [16] and earlier editions of the ‘Particle Data Book’). The SMPP contains a finite number of parameters, which are unrelated, at least within the context of the theory itself. One imagines that a more complete theory of fundamental physics will explain the relationships among these parameters. The ultimate goal would be to determine the values of the parameters from pure mathematics, once the correct theory is discovered. It may also be that some of the parameters have a stochastic origin, where our Universe is one choice from among an array of possible vacuum states. This used to be called Anthropic reasoning (see e.g. [5, 50, 7]), and received such little respect from many scientists that it became known as ‘the A word’, and would elicit groans at conDouglas Scott. Department of Physics & Astronomy, University of British Columbia, Vancouver, B.C., V6T1Z1, Canada. e-mail: [email protected] Can. J. Phys. : 1–16 () NRC Canada 2 Can. J. Phys. Vol. , Table 1. The 26 Parameters of the Standard Model of Particle Physics. 6 quark masses: mu md ms mc mt mb 4 quark mixing angles: θ12 θ23 θ13 δ 6 lepton masses: me mμ mτ mνe mνμ mντ 4 lepton mixing angles: θ′ 12 θ ′ 23 θ ′ 13 δ ′ 3 electroweak parameters: α GF MZ 1 Higgs mass: mH 1 strong CP violating phase: θ̄ 1 QCD coupling constant: αS(MZ) 26 total parameters ferences. But now string theorists have renamed it ‘the Landscape’ [61] and given it some theoretical basis. Although these ideas may now have a little more mainstream credibility (and are discussed in a later section), still not everyone agrees that it is a worthy avenue of inquiry.1 The number of parameters within the standard model varies slightly among phenomenologists, depending on precisely how minimal the model under consideration is, and, in particular, how the neutrinos are treated. A popular counting exercise gives 19 parameters in the minimal SMPP, plus 7 additional quantities to describe the neutrino sector. This is shown in Table 1. There are 26 free parameters in this model; if we were to develop the SMPP from scratch, then presumably we would label the parameters as A, B, C, . . . , Z . Given this proliferation of numbers, one expects that, for the sake of elegance, there must be a more fundamental theory with far fewer parameters. As is well known, the SMPP has been astonishingly successful, so much so that, for the last 3 decades, the emphasis has been on trying to find inadequacies in it – i.e. searching for ‘physics beyond the standard model’. However, apart from theoretical ideas (some of them admittedly quite appealing), there are still no convincing pieces of evidence for physics beyond the SMPP. On the other hand, we know that there has to be new physics, beyond the SMPP, due to what we have learned about the properties of the large-scale Universe – particularly cosmological evidence for dark matter, dark energy and inflation. Cosmology grew from being an arm-chair activity carried out in people’s spare time, to being a dignified scientific pursuit, only in the 1960s. Originally the models were entirely baryonic and involved simple ad hoc initial conditions. In many ways the basic picture has remained the same since then – nearly scale invariant and adiabatic initial conditions, in an almost isotropic and homogeneous Friedmann-Robertson-Walker solution to Einstein’s Field Equations. However, Cold Dark Matter was added to the paradigm in the 1980s (e.g. [43, 6]), leading to the ‘Standard CDM’ picture in which ΩM = 1. By the end of the 1980s the addition of a cosmological constant Λ was known to give better fits to the available data (e.g. [44, 65, 15]). The COBE satellite detection of large-scale Cosmic Microwave Background (CMB) anisotropies in 1992 [58] brought an end to many wilder proposals which had been floated in the era of continually improving CMB upper limits (see [36] for a discussion). It became clear that the CMB normalization, together with galaxy clustering data, pointed to the ‘ΛCDM’ variant of the CDM paradigm ([14, 31]), despite the reluctance of many theorists to let the elegance of Standard CDM slip away (e.g. [67]). The cosmological constant became an accepted part of the model by the mid-to-late 1990s, following the results from distant supernova surveys and degree-scale CMB experiments. Soon the concept of Λ was generalised to that of Dark Energy. As the CMB anisotropy measurements grew increasingly precise, 1 And it has become known as ‘the other L word’.