Scalar correlation functions in de Sitter space from the stochastic spectral expansion

We consider light scalar fields during inflation and show how the stochastic spectral expansion method can be used to calculate two-point correlation functions of an arbitrary local function of the field in de Sitter space. In particular, we use this approach for a massive scalar field with quartic self-interactions to calculate the fluctuation spectrum of the density contrast and compare it to other approximations. We find that neither Gaussian nor linear approximations accurately reproduce the power spectrum, and in fact always overestimate it. For example, for a scalar field with only a quartic term in the potential, $V=\lambda\phi^4/4$, we find a blue spectrum with spectral index $n-1=0.579\sqrt{\lambda}$.Comment: 21 pages, 4 figures, 2 tables. v2: minor revision, version published in JCA

From the Logic of Science to the Logic of the Living

Biosemiotics belongs to a class of approaches that provide mental models of life since it applies some semiotic concepts in the explanation of natural phenomena. Such approaches are typically open to anthropomorphic errors. Usually, the main source of such errors is the excessive vagueness of the semiotic concepts used. If the goal of biosemiotics is to be accepted as a science and not as a priori metaphysics, it needs both an appropriate source of the semiotic concepts and a reliable method of adjusting them for biosemiotic use. Charles S. Peirce’s philosophy offers a plausible candidate for both these needs. Biosemioticians have adopted not only Peirce’s semiotic concepts but also a number of metaphysical ones. It is shown that the application of Peirce’s basic semiotic conceptions of sign and sign-process (semiosis) at the substantial level of biosemiotics requires the acceptance of certain metaphysical conceptions, i.e. Tychism and Synechism. Peirce’s method of pragmaticism is of great relevance to biosemiotics: 1. Independently of whether Peirce’s concepts are used or even applicable at the substantial level of biosemiotics, Peirce’s method remains valuable in making biosemiotics and especially in adjusting its basic concepts. 2. If Peircean semeiotic or metaphysics is applied at the substantial level of biosemiotics, pragmaticism is valuable in clarifying the meaning and reference of the applied Peircean concepts. As a consequence, some restrictions for the application of Peirce in biosemiotics are considered and the distinction of Peirce’s philosophy from the 19th century idealistic Naturphilosophie is emphasized

De Sitter Stability and Coarse Graining

We present a 4-dimensional back reaction analysis of de Sitter space for a conformally coupled scalar field in the presence of vacuum energy initialized in the Bunch-Davies vacuum. In contrast to the usual semi-classical prescription, as the source term in the Friedmann equations we use expectation values where the unobservable information hidden by the cosmological event horizon has been neglected i.e. coarse grained over. It is shown that in this approach the energy-momentum is precisely thermal with constant temperature despite the dilution from the expansion of space due to a flux of energy radiated from the horizon. This leads to a self-consistent solution for the Hubble rate, which is gradually evolving and at late times deviates significantly from de Sitter. Our results hence imply de Sitter space to be unstable in this prescription. The solution also suggests dynamical vacuum energy: the continuous flux of energy is balanced by the generation of negative vacuum energy, which accumulatively decreases the overall contribution. Finally, we show that our results admit a thermodynamic interpretation which provides a simple alternate derivation of the mechanism. For very long times the solutions coincide with flat space.Comment: v6: added an appendix giving details on mode normalizatio

Limitations on applying Peircean semeiotic. Biosemiotics as applied objective ethics and esthetics rather than semeiotic.

This paper explores the critical conditions of such semiotic realism that is commonly presumed in the so-called Copenhagen interpretation of biosemiotics. The central task is to make basic biosemiotic concepts as clear as possible by applying C.S. Peirce’s pragmaticist methodology to his own concepts, especially to those that have had a strong influence on the Copenhagian biosemiotics. It appears essential to study what kinds of observation the basic semiotic concepts are derived from. Peirce had two different derivations to the concept of sign, both having a strong logical character. Therefore, it is discussed at length what Peirce’s conception of logic consists of and how logical concepts relate to the concepts of other sciences. It is shown that Peirce had two different perspectives toward sign, the ‘transcendental’ one and the objective one, and only the latter one is executable in biosemiotic applications. Although Peirce’ theory of signs seems to appear as twofold (if not even manifold), it is concluded that the ore conception has been stable. The apparent differences are presumably due to the different perspectives of consideration. Severe limitations for the application of Peirce’s semiotic concepts follow from this analysis that should be taken into account in biosemiotics relying on its Copenhagen interpretation. The first one concerns the ‘interpreter’ of a suggested biosemiotic sign — whether it is ‘we’ (as a ‘meta-agent’) or some genuine biosemiotic ‘object-agent’. Only if the latter one is determinable, some real biosemiotic sign-action may occur. The second one concerns the application of the concept of the object of sign — its use is limited so that a sign has an object if and only if it seeks a true conception about it. This conclusion has drastic further consequences. Most of the genuinely biosemiotic sign-processes do not tend toward truth about anything but toward various practical ends. Therefore, the logical concept of sign, e.g. the one of Peirce’s semeiotic, is an insufficient concept for biosemiotics. In order to establish a sufficient one, Peircean theoretical ethics and esthetics are introduced. It is concluded that they involve simpler and more general but still normative concept of sign — the concept of anticipative or constructive representation that does not represent any object at all. Instead, it is a completely future-oriented representation that guides action. Objective ethics provides the suitable concept of representation, but it appeals to objective esthetics that provides a theory of (local) natural self-normativity. The concepts of objective logic form the special species of objective ethics. The conclusion is that biosemiotics should be based on applied objective ethics and esthetics rather than on (Peircean semeiotic) logic and its metaphysical application. Finally, the physiosemiotic over-generalization of the concept of sign is shortly discussed. It is suggested that it would be more appropriate to rename such controversial generalizations than to adhere to semiotic terminology. Here, again, Peirce appears as a healthy role model with his ‘ethics of terminology’

Vacuum alignment and radiatively induced Fermi scale

We extend the discussion about vacuum misalignment by quantum corrections in models with composite pseudo-Goldstone Higgs boson to renormalisable models with elementary scalars. As a concrete example, we propose a framework, where the hierarchy between the unification and the Fermi scale emerges radiatively. This scenario provides an interesting link between the unification and Fermi scale physics.Comment: 7 pages. To appear in the proceedings of the 5th International Conference on New Frontiers in Physics ICNFP2016, July 06 - 14, 2016. Based on arXiv:1511.01910 and arXiv:1608.07442. arXiv admin note: text overlap with arXiv:1609.0849

Renormalization of the inflationary perturbations revisited

In this work we clarify aspects of renormalization on curved backgrounds focussing on the potential ramifications on the amplitude of inflationary perturbations. We provide an alternate view of the often used adiabatic prescription by deriving a correspondence between the adiabatic subtraction terms and traditional renormalization. Specifically, we show how adiabatic subtraction can be expressed as a set of counter terms that are introduced by redefining the bare parameters of the action. Our representation of adiabatic subtraction then allows us to easily find other renormalization prescriptions differing only in the finite parts of the counter terms. As our main result, we present for quadratic inflation how one may consistently express the renormalization of the spectrum of perturbations from inflation as a redefinition of the bare cosmological constant and Planck mass such that the observable predictions coincide with the unrenormalized result.Comment: v1: 17 pages. v2: 17 pages, minor improvements, updated references. v3: 19 pages, added discussion, version accepted for publication in JCA

Optimal forest rotation age under efficient climate change mitigation

This paper considers the optimal rotation of forests when the carbon flows of forest growth and harvest are priced with an increasing price. Such an evolution of carbon price is generally associated with economically efficient climate change mitigation, and would provide incentives for the land-owner for enhanced carbon sequestration. With an infinitely long sequence of even-aged forest rotations, the optimal harvest age changes with subsequent rotations due to the changing carbon price. The first-order optimality conditions therefore also involve an infinite chain of lengths for consecutive forest rotations, and allow the approximation of the infinite-time problem with a truncated series of forest rotations. Illustrative numerical calculations show that when starting from bare land, the initial carbon price and its growth rate both primarily increase the length of the first rotation. With some combinations of the carbon pricing parameters, the optimal harvest age can be several hundred years if the forest carbon is released to the atmosphere upon harvest. This effect is not, however, entirely monotonous. Consequently, the currently optimal harvest ages are generally lower with higher rates of carbon price increase. This creates an interesting temporal aspect, suggesting that the supply of wood and carbon sequestration by forests can change considerably during subsequent rotations under an increasing price on carbon.Comment: in Forest Policy and Economics, 201