Bibliography on Philosophy of Cosmology

An essential text in the philosophy of statistical mechanics, this book provides an argument that statistical mechanics only allows us to retrodict from the present if we include a “Past Hypothesis” that the initial state of the universe was one of extremely low entropy. Albert’s book has sparked much philosophical interest in cosmology, especially over the sorts of initial states deemed acceptable for compatibility with local physics.

Callender provides a comprehensive overview of gravitational statistical mechanics, and highlights some of the supposed paradoxes that might arise. He argues that these supposed paradoxes can consistently be handled, and that they raise many philosophical issues that are largely neglected by philosophers of physics.

A critical response to Albert’s program, Earman argues that the Boltzmann entropy of the early universe is not a well-defined concept, and that even if the early universe had a well-defined low Boltzmann entropy, this would not suffice to explain why all local systems have the same arrow of time.

Proposes that the presence of spacetime singularities in generic solutions of general relativity holds the key to solving the problem of time’s arrow. Includes detailed discussion of the problem of time’s arrow, cosmic censorship, and gravitational entropy, as well as an initial formulation of the Weyl curvature hypothesis.

A recent take on the issue of time’s arrow in cosmology, Rovelli argues that the universe need not have been in a particularly low entropy – and therefore improbable – initial state in order for the entropy gradient in the observable universe to provide an arrow of time. In a large enough universe, Rovelli argues that some subregions according to which the entropy is low in the past direction.

Wallace argues that attempts to understand the near-uniform state of the early universe as low entropy states due to the tendency of gravitational collapse are confused. In particular, one should not think of the entropy in gravitational degrees of freedom as having any relevance for the out of equilibrium processes that we observe in our local spacetime region.

Wallace proposes an amendment to the way of thinking about the Past Hypothesis stemming from Albert. Rather than attempting to reconcile our psychological experience of time asymmetry with the time reversal invariance of the fundamental laws of physics, Wallace suggests that we limit the scope of the argument to reconciling the time irreversibility of emergent (i.e., non-fundamental) laws of physics with the reversibility of the fundamental laws.

This paper explores how the possibility of a multiverse affects the quantum measurement problem. More specifically, it provides a derivation of the Born Rule à la de Witt from the relative frequencies of infinitely many observers in a universe so big that every outcome of an experiment is always realized. This paper is a good starting point for those interested by the problems arising for Many-Worlds interpretations of Quantum Mechanics in a cosmological context.

Gell-Mann and Hartle discusses the implications of cosmology, and more specifically of the idea of a quantum-mechanical description of the universe as a whole, for interpretation of quantum mechanics.

In the ΛCDM model, large-scale structures arise from primordial density fluctuations of a quantum origin. This paper critically discusses this thesis and emphasizes the physics that is still lacking to explain how quantum-mechanical uncertainties can turn a perfectly homogeneous and isotropic state into an inhomogeneous, anistropic one.

Wallace argues that the Everett interpretation is the only interpretation that makes sense of how quantum theory is used in cosmology. According to Wallace, this provocative claim follows from the fact that conceptual difficulties related to the measurement problem and to the definition of an “outside-measurement context” undermine other approaches to interpreting quantum theory in cosmology.

Critically reviews two arguments regarding the possibility of introducing a notion of global cosmic time in relativistic cosmological models.

Physics review article regarding the cosmological impact of a wide variety of modifications of general relativity.

Influential systematic overview of foundational questions prompted by singularities and other aspects of causal structure in general relativity

Excellent review of the concepts of global causal structure developed in the 1960s – 70s.

Proposes several variations and refinements on a definition of “observationally indistinguishable” spacetimes, originally due to Glymour.  Proves a number of results regarding the invariance of global spacetime properties under different versions of indistinguishability.

 In this article, Manchak proves how little local observers can know about the global structure of spacetime in the context of general relativity. In particular, he shows that, for almost any cosmological model, no amount of local data could ever single it out as the unique model accurately describing our universe. Even if one assumes a principle of uniformity of physical laws, major epistemological issues still remain. In a certain sense, our cosmological models are therefore completely underdetermined, even when the background theory of gravity is specified in advance.

It is common in cosmology to assume that we have a well-defined notion of cosmic time up until a Planck time (10^-43s) “after” the big bang. Rugh and Zinkernagel provide arguments that our concepts of time break down far earlier in a backwards extrapolation. Depending on the assumptions, cosmic time either breaks down at the hadron-quark phase transition, at the electroweak phase transition, or at the onset of inflation.

Considers the role of the conservation condition in establishing the geodesic principle in general relativity.  Further argues that the conservation condition should be understood as following from the dynamical equations governing the evolution of matter.

Loop quantum cosmology is a simplified form of loop quantum gravity, restricted to highly symmetric spacetimes. When spacetime is quantized, big bang and big crunch singularities are avoided. This article provides an overview of singularity resolution results from the loop quantum cosmology community.

The classic paper in which the formalism of Wheeler-DeWitt geometrodynamics and superspace is introduced. This formalism is an attempt to merge ordinary quantum theory with general relativity.

A different approach to quantum cosmology, starting with a Lorentzian form of the path-integral, rather than the Euclidean form used in the classic Wheeler-DeWitt formalism. Using Picard-Lefschetz theory, the Lorentzian path-integral is converted to an absolutely convergent integral, whose saddle point approximation is the negative of the standard Wheeler-DeWitt result.

A wave function for spatially closed universe that obeys the second order Wheeler-DeWitt equation is derived. The wavefunction is defined over the space of compact three-manifolds. An important paper in the history of quantum gravity, and a good presentation of the constrained Hamiltonian formalism shared by many approaches to quantum gravity.

Using the formalism of covariant loop quantum gravity, Rovelli and Vidotto show that there is an upper limit to acceleration allowed, related to the discreteness of spacetime. Since acceleration cannot diverge, this result shows that curvature singularities do not arise in general loop quantum gravity. Aimed at a specialist audience.

Theories of quantum gravity often dispense with space and time at a fundamental level.  This paper considers how space time is recovered in loop quantum gravity, and illustrates an approach to debates regarding “emergence” of spacetime.