# Calculating Observable Universe Mass in the Lambda-CDM Model

• Orion1
In summary, the conversation discusses the equation for the observable Universe mass based on the Lambda-CDM model and observational parameters from the Hubble Space Telescope (HST) and WMAP in SI units. The equation takes into account the Hubble parameter, baryon density, dark matter density, observable stellar number and volume, and solar mass. The conversation also mentions the stellar baryon density, total matter density, and cosmological critical density. The speaker questions the implications of the calculated observable Universe mass being greater than the Hubble critical mass and asks for confirmation of the correctness of their equations and calculations.

#### Orion1

This is my equation for the Universe mass based upon the Lambda-CDM model parameters and the Hubble Space Telescope (HST) and WMAP observational parameters in SI units.

Observable Universe mass composition:
$$H_0 = 2.32987690448613 \cdot 10^{- 18} \; \text{s}^{- 1}$$ - Hubble parameter (WMAP)
$$\Omega_b = 0.00444$$ - Baryon density
$$\Omega_{dm} = (\Omega_m - \Omega_b) = 0.2216$$ - dark matter density
$$dN_s = 10^{22}$$ - HST observable stellar number
$$dV_s = 3.3871 \cdot 10^{78} \; \text{m}^3 \; \; \; (4 \cdot 10^{30} \; \text{ly}^3)$$ - HST observable stellar volume
$$M_{\odot} = 1.9891 \cdot 10^{30} \; \text{kg}$$ - solar mass

Observable Universe mass:
$$\boxed{M_u = \frac{4 \pi M_{\odot}}{3 \Omega_b} \left( \frac{dN_s}{dV_s} \right) \left( \frac{c}{H_0} \right)^3}$$

$$\boxed{M_u = 1.18029735794067 \cdot 10^{55} \; \text{kg}}$$

Gravitationally observable dark matter mass:
$$\boxed{M_{dm} = \frac{4 \pi M_{\odot}}{3} \left( \frac{\Omega_{dm}}{\Omega_b} \right) \left( \frac{dN_s}{dV_s} \right) \left( \frac{c}{H_0} \right)^3}$$

$$\boxed{M_{dm} = 2.61553894519654 \cdot 10^{54}}$$

Hubble critical mass:
$$\boxed{M_c = \frac{c^3}{2 G H_0}}$$
$$\boxed{M_c = 8.66352589042757 \cdot 10^{52} \; \text{kg}}$$

Reference:
"[URL [Broken] law - Wikipedia[/URL]
http://en.wikipedia.org/wiki/Lambda-CDM_model" [Broken]
http://en.wikipedia.org/wiki/Universe" [Broken]
http://en.wikipedia.org/wiki/Observable_universe" [Broken]
http://en.wikipedia.org/wiki/Dark_matter" [Broken]

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Correction, the Baryon density listed in post #1 is the stellar Baryon density, not the total Baryon density.

The stellar Baryon density ranges between:
$$\Omega_s = \int_{0.004}^{0.005}$$

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$$\Omega_s = 0.005$$ - stellar Baryon density

Observable Universe mass:
$$\boxed{M_u = \frac{4 \pi M_{\odot}}{3 \Omega_s} \left( \frac{dN_s}{dV_s} \right) \left( \frac{c}{H_0} \right)^3}$$

$$\boxed{M_u = 1.04810405385132 \cdot 10^{55} \; \text{kg}}$$

Gravitationally observable dark matter mass:
$$\boxed{M_{dm} = \frac{4 \pi M_{\odot}}{3} \left( \frac{\Omega_{dm}}{\Omega_s} \right) \left( \frac{dN_s}{dV_s} \right) \left( \frac{c}{H_0} \right)^3}$$

$$\boxed{M_{dm} = 2.32259858333452 \cdot 10^{54} \; \text{kg}}$$

Hubble critical mass:
$$\boxed{M_c = \frac{c^3}{2 G H_0}}$$

$$\boxed{M_c = 8.66352589042757 \cdot 10^{52} \; \text{kg}}$$

Observable Universe mass greater than or equal to Hubble critical mass:
$$\boxed{M_u \geq M_c}$$

$$\boxed{\frac{4 \pi M_{\odot}}{3 \Omega_s} \left( \frac{dN_s}{dV_s} \right) \left( \frac{c}{H_0} \right)^3 \geq \frac{c^3}{2 G H_0}}$$

Observable Universe mass equivalent to Hubble critical mass:
$$\boxed{M_u = M_c}$$

$$\frac{4 \pi M_{\odot}}{3 \Omega_s} \left( \frac{dN_s}{dV_s} \right) \left( \frac{c}{H_0} \right)^3 = \frac{c^3}{2 G H_0}$$

Observable critical stellar Baryon density:
$$\boxed{\Omega_s = \frac{8 \pi G M_{\odot}}{3 H_0^2} \left( \frac{dN_s}{dV_s} \right)}$$

$$\boxed{\Omega_s = 0.604894627838177}$$

Total matter density:
$$\Omega_m = 0.266$$

According to my calculations, the observable Universe mass is greater than the Hubble critical mass.

What exactly are the cosmological theoretical implications for this criteria?

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Observable stellar Baryon critical density:
$$\Omega_s = 0.604894627838177$$

Observable cosmological critical density:
$$\Omega_{\Lambda} = 0.7$$

Reference:
http://en.wikipedia.org/wiki/Lambda-CDM_model" [Broken]

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Why don't you google 'Hubble critical mass' and publish 'your' results in an article?

malawi_glenn said:
Why don't you google 'Hubble critical mass' and publish 'your' results in an article?

All my equations require proofreading by a peer review, prior to any publication.

According to my calculations, the observable Universe mass is greater than the Hubble critical mass.

What exactly are the theoretical cosmological implications for this criteria?

Are my equations and calculations correct?

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## 1. What is the Lambda-CDM model and why is it important in calculating the observable universe mass?

The Lambda-CDM model is a cosmological model that describes the evolution of the universe. It is based on the theory of general relativity and includes the presence of dark energy (represented by the Greek letter lambda) and cold dark matter (represented by CDM). This model is important in calculating the observable universe mass because it provides a framework for understanding the large-scale structure of the universe and the distribution of matter within it.

## 2. How is the observable universe mass calculated in the Lambda-CDM model?

The observable universe mass is calculated by using various measurements and observations of the universe, such as the cosmic microwave background radiation, the distribution of galaxies, and the expansion rate of the universe. These measurements are then plugged into mathematical equations derived from the Lambda-CDM model to estimate the total mass of the observable universe.

## 3. What is the current estimated mass of the observable universe according to the Lambda-CDM model?

According to recent calculations using the Lambda-CDM model, the estimated mass of the observable universe is about 10^53 kilograms. This includes both ordinary matter (such as atoms and molecules) and dark matter, but does not include dark energy, which is believed to make up about 70% of the total mass of the universe.

## 4. How does the Lambda-CDM model account for the effects of dark energy and dark matter on the observable universe mass?

The Lambda-CDM model takes into account the effects of dark energy and dark matter by including them in its equations and calculations. Dark energy is thought to contribute to the overall expansion of the universe, while dark matter plays a crucial role in the formation of large-scale structures like galaxies and galaxy clusters. Both of these components are necessary to accurately calculate the observable universe mass in the Lambda-CDM model.

## 5. Are there any limitations or uncertainties in using the Lambda-CDM model to calculate the observable universe mass?

Like any scientific model, the Lambda-CDM model has its limitations and uncertainties. One major limitation is that it assumes the universe is homogeneous and isotropic on a large scale, which may not be entirely accurate. Additionally, the exact nature of dark energy and dark matter is still not fully understood, which can introduce uncertainties in the calculations. However, the Lambda-CDM model is currently the best framework we have for understanding and estimating the observable universe mass.