scholarly journals On the perturbative expansion at high temperature and implications for cosmological phase transitions

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
Oliver Gould ◽  
Tuomas V. I. Tenkanen
Keyword(s):  
Phase Transitions ◽  
High Temperature ◽  
Effective Potential ◽  
Bubble Nucleation ◽  
Perturbative Expansion ◽  
Zero Temperature ◽  
Loop Order ◽  
First Order ◽  
First Order Phase ◽  
Renormalisation Scale

Abstract We revisit the perturbative expansion at high temperature and investigate its convergence by inspecting the renormalisation scale dependence of the effective potential. Although at zero temperature the renormalisation group improved effective potential is scale independent at one-loop, we show how this breaks down at high temperature, due to the misalignment of loop and coupling expansions. Following this, we show how one can recover renormalisation scale independence at high temperature, and that it requires computations at two-loop order. We demonstrate how this resolves some of the huge theoretical uncertainties in the gravitational wave signal of first-order phase transitions, though uncertainties remain stemming from the computation of the bubble nucleation rate.

scholarly journals Theoretical uncertainties for cosmological first-order phase transitions

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Djuna Croon ◽  
Oliver Gould ◽  
Philipp Schicho ◽  
Tuomas V. I. Tenkanen ◽  
Graham White
Keyword(s):  
Phase Transitions ◽  
Standard Model ◽  
Scale Dependence ◽  
Effective Field ◽  
Bubble Nucleation ◽  
Perturbative Approach ◽  
First Order ◽  
The Standard Model ◽  
First Order Phase ◽  
Renormalisation Scale

Abstract We critically examine the magnitude of theoretical uncertainties in perturbative calculations of fist-order phase transitions, using the Standard Model effective field theory as our guide. In the usual daisy-resummed approach, we find large uncertainties due to renormalisation scale dependence, which amount to two to three orders-of-magnitude uncertainty in the peak gravitational wave amplitude, relevant to experiments such as LISA. Alternatively, utilising dimensional reduction in a more sophisticated perturbative approach drastically reduces this scale dependence, pushing it to higher orders. Further, this approach resolves other thorny problems with daisy resummation: it is gauge invariant which is explicitly demonstrated for the Standard Model, and avoids an uncontrolled derivative expansion in the bubble nucleation rate.

Bubble nucleation rates in first-order phase transitions

1993 ◽  
Vol 48 (10) ◽  
pp. 6788-6794 ◽  
Author(s):  
W. N. Cottingham ◽  
D. Kalafatis ◽  
R. Vinh Mau
Keyword(s):  
Phase Transitions ◽  
Bubble Nucleation ◽  
First Order ◽  
First Order Phase

scholarly journals Bubble-nucleation rates for radiatively induced first-order phase transitions

1999 ◽  
Vol 554 (3) ◽  
pp. 697-718 ◽  
Author(s):  
Alessandro Strumia ◽  
Nikolaos Tetradis
Keyword(s):  
Phase Transitions ◽  
Bubble Nucleation ◽  
First Order ◽  
First Order Phase

scholarly journals PHASE TRANSITIONS FOR A ϕ6 MODEL IN (2+1)-DIMENSIONAL CURVED SPACETIME

2003 ◽  
Vol 18 (13) ◽  
pp. 937-946 ◽  
Author(s):  
MINU JOY ◽  
V. C. KURIAKOSE
Keyword(s):  
Phase Transitions ◽  
Effective Potential ◽  
Momentum Tensor ◽  
Type I ◽  
Curved Spacetime ◽  
First Order ◽  
Spacetime Curvature ◽  
First Order Phase Transition ◽  
The One ◽  
First Order Phase

Considering a massive ϕ6 self-interacting scalar field coupled arbitrarily to a (2+1)-dimensional Bianchi type-I spacetime, we evaluate the one-loop effective potential. It is found that ϕ6 potential can be regularized in (2+1)-dimensional curved spacetime. A finite expression for the energy–momentum tensor is obtained for this model. Evaluating the finite temperature effective potential, the temperature dependence of phase transitions is studied. The crucial dependence of the phase transitions on the spacetime curvature and on the coupling to gravity is also studied. The nature of phase transitions for the present model is clarified to be first order. A first-order phase transition proceeds by nucleation of bubbles of broken phase in the background of unbroken phase.

scholarly journals Gravitational waves from first-order phase transitions: towards model separation by bubble nucleation rate

2017 ◽  
Vol 2017 (11) ◽  
pp. 050-050 ◽  
Author(s):  
Ryusuke Jinno ◽  
Sangjun Lee ◽  
Hyeonseok Seong ◽  
Masahiro Takimoto
Keyword(s):  
Phase Transitions ◽  
Gravitational Waves ◽  
Nucleation Rate ◽  
Bubble Nucleation ◽  
First Order ◽  
First Order Phase

scholarly journals Effective potential and first-order phase transitions: Beyond leading order

1993 ◽  
Vol 47 (8) ◽  
pp. 3546-3579 ◽  
Author(s):  
Peter Arnold ◽  
Olivier Espinosa
Keyword(s):  
Phase Transitions ◽  
Effective Potential ◽  
Leading Order ◽  
First Order ◽  
First Order Phase

scholarly journals THE EXACT RENORMALIZATION GROUP AND FIRST-ORDER PHASE TRANSITIONS

2001 ◽  
Vol 16 (11) ◽  
pp. 1927-1939 ◽  
Author(s):  
N. TETRADIS
Keyword(s):  
Renormalization Group ◽  
Phase Transitions ◽  
Scalar Fields ◽  
Bubble Nucleation ◽  
Nucleation Theory ◽  
Three Dimensional Model ◽  
Exponential Factor ◽  
First Order ◽  
Exact Renormalization Group ◽  
First Order Phase

Studies of first-order phase transitions through the use of the exact renormalization group are reviewed. In the first part the emphasis is on universal aspects: We discuss the universal critical behaviour near weakly first-order phase transitions for a three-dimensional model of two coupled scalar fields – the cubic anisotropy model. In the second part we review the application of the exact renormalization group to the calculation of bubble-nucleation rates. More specifically, we concentrate on the pre-exponential factor. We discuss the reliability of homogeneous nucleation theory that employs a saddle-point expansion around the critical bubble for the calculation of the nucleation rate.

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