First off, there is nothing "perpetual" about increases in GNP, it rises, it falls, it rises again. Second, the simple answer is growth can continue with a stable population as long as productivity rises (output per person). Third "perpetual economic growth" defined absurdly as it is as "more", is not a utopia, its a nightmare, a dystopia. Ever increasing GDP is just more and more "stuff" - the vast majority of which is produced only to keep people working - the primary form of capitalist control over society. Redefined to take quality into account, as is usually the case in the idea of "development" (vs growth) then there's no reason why multidimensional increases in many different qualities can't go on as long as people desire. Changes in quantity depend on the quality being measured. GDP only measures ONE quality (market value of commodities). Escape that reductionist summation of human activity and replace it with a wide variety of desirable "qualities" and you need an equally wide variety of measures of "growth".

Is perpetual economic growth a utopia?

The first answer was quite adequate, but I will clarify where I see the need.

To start, population growth is projected to stabilize with or without global warming, at around 10 billion people, depending on the rate of economic growth and political action, due to the decline in fertility rates as gdp/capita rises. This is due to a number of factors; access to contraception, education and gender equality, less economic need for many children. Certainly change is needed for a cooler planet, but that could be less people, lower greenhouse gas emission per person, or greater carbon sequestering. There are other environmental problems, like plastic pollution, which can be tackled with the same options - decreased consumption (and therefore less waste), less waste per person (new technology, lifestyle change, regulation), or plastic cleanup.

There is constant competition between companies for dominance. Productivity enhancing technology enables competitive advantage and produces more per person, so gdp can increase this way even with a stable population. Total gdp is not as important as gdp/capita if you're interested in what's now considered an indicator for well being. That only increases with productivity. The real question of well being is not even gdp/capita, it's distribution of wealth. We now have very high inequality and many people without basic needs met.

The short answer is that utopia is possible without population growth or productivity growth even now, but it's dependent upon power and allocation, which is heavily slanted towards owners of capital (vast minority) in our capitalist society. Perpetual economic growth depends on the measurement of growth, and GDP has minimal direct impact on well being or happiness.

The global economy and population will continue to grow, despite how disproportionate or proportionate both may be growing. World population is growing at about 1.08% per year, although it is not steady and often fluctuates. The world economic growth is at about 3.6% per year; it also fluctuates.

Both will continue to grow year after year.